% lippolis/bibtex/lippolis.bib
% $Author: domenico $ $Date: 2012-10-18 02:55:10 -0400 (Thu, 18 Oct 2012) $
% **************************************************************************
% Predrag is entering new references at the top of this file
% move them where you want them
% Predrag transfered Graham, Haken refs from Mar 13 2010
% articles/bibtex/FogedbyArticles.bib
% remember, more references are in
% articles/bibtex/noise.bib
% Predrag added gasp02 Sep 18 2005
% Vaggelis Sep 13 2005
% Predrag Sep 5 2005
% included waleffebib.bib, Waleffe bibliography Sep 4 2005
% ../y-lan/bibtex/nonlind.bib Dec 29 2004
ARTICLE{,
author = {},
title = {},
journal = {},
volume = {},
pages = {},
year = {},
abstract = {}
}
BOOK{,
author = {},
title = {},
publisher = {},
address = {},
year = {}
}
%%%%%%%%%%%%%%%% Predrag's new additions %%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%% move them elsewhere, if you want to reorganize
@ARTICLE{ApStVo07,
author = {Apte, A and Hairer, M. and Stuart, A. and Voss, J.},
title = {Sampling the posterior: {An}
approach to non-{Gaussian} data assimilation},
journal = {Physica D},
volume = {230},
pages = {50--64},
year = {2007}
}
@ARTICLE{Cox64,
author = {Cox, H.},
title = {On the estimation of state variables and
parameters for noisy dynamic systems},
journal = {IEEE Trans. Auto. Contr.},
volume = {9},
pages = {5--12},
year = {1964}
}
@MISC{Frasca12,
author = {Frasca, M.},
title = "Quantum mechanics is the square root of a stochastic process",
note = {\arXiv{1201.5091}},
year = {2012}
}
@ARTICLE{FrBe66,
author = {Friedland, B. and Bernstein, I.},
title = {Estimation of the state of a nonlinear process
in the presence of non-{Gaussian} noise and disturbances},
journal = {J. Franklin. Inst.},
volume = {281},
pages = {455--480},
year = {1966}
}
@Misc{BoGaMcK09,
author = {Boland, R. P. and Galla, T. and {McKane}, A. J.},
title = {Limit cycles, complex {Floquet} multipliers
and intrinsic noise},
note = {\arXiv{0903.5248}},
abstract = {We study the effects of intrinsic noise on
chemical reaction systems, which in the deterministic limit
approach a limit cycle in an oscillatory manner. Previous
studies of systems with an oscillatory approach to a fixed
point have shown that the noise can transform the oscillatory
decay into sustained coherent oscillations with a large
amplitude. We show that a similar effect occurs when the
stable attractors are limit cycles. We compute the
correlation functions and spectral properties of the
fluctuations in suitably co-moving Frenet frames for several
model systems including driven and coupled Brusselators, and
the {Willamowski-Roessler} system. The effect occurs whenever
the Floquet multipliers of the limit cycle are complex, with
the amplitude of the oscillations increasing as the
instability boundary is approached.},
year = {2009},
}
@Book{Lichtenberg92,
author = { A. J. Lichtenberg and M. A. Lieberman},
title = { Regular and Chaotic Dynamics},
publisher = {{S}pringer-{V}erlag},
year = 1992,
address = {N.Y.}
}
@ARTICLE{RechWhi91,
TITLE = "Symbolic Kinetic-Equation for a Chaotic Attractor ",
AUTHOR = "A. B. Rechester and R. B. White ",
JOURNAL = "Phys. Lett. A",
VOLUME = "156",
PAGES = "419-424",
YEAR = "1991"
}
@ARTICLE{RechWhi91maps,
TITLE = "Symbolic Kinetic Analysis of Two-Dimensional Maps ",
AUTHOR = "A. B. Rechester and R. B. White ",
JOURNAL = "Phys. Lett. A",
VOLUME = "158",
PAGES = "51-56",
YEAR = "1991"
}
@MISC{Nico90,
author = {G. Nicolis},
title = {Chaotic dynamics and markovian coarse-graining in
nonlinear dynamical systems},
note = {in \textit{Noise and Chaos in Nonlinear Dynamical Systems},
edited by F. Moss, L. A. Lugiato, and W. Schleich
(Cambridge University Press)},
year = {1990}
}
@ARTICLE{Nico95,
author = {J. S. Nicolis},
title = {Chaotic dynamics applied to information processing},
journal = {Rep. Prog. Phys.},
volume = {49},
pages = {1109-1196},
year = {1986},
}
@article{AltTel08,
author = {Altmann, E. G. and T\'el, T.},
title = {Poincar\'e recurrences and transient chaos in systems with leaks},
journal = {Phys. Rev. E},
volume = {79},
pages = {016204},
numpages = {12},
abstract = {Simulating observational and experimental
situations, we consider a leak in the phase space of a chaotic
dynamical system. We obtain an expression for the escape rate
of the survival probability applying the theory of transient
chaos. This expression improves previous estimates based on the
properties of the closed system and explains dependencies on
the position and size of the leak and on the initial ensemble.
With a subtle choice of the initial ensemble, we obtain an
equivalence to the classical problem of Poincare recurrences in
closed systems, which is treated in the same framework.
Finally, we show how our results apply to weakly chaotic
systems and justify a split of the invariant saddle in
hyperbolic and non-hyperbolic components, related,
respectively, to the intermediate exponential and asymptotic
power-law decays of the survival probability.},
note = {\arXiv{0808.3785}},
year = {2009},
}
@ARTICLE{HolstKa08,
author = {Holstein, D. and Kantz, H.},
title = {Optimal {Markov} approximations and generalized embeddings},
journal = {Phys. Rev. E},
volume = {79},
pages = {056202},
year = {2009},
abstract = {Based on information theory, we present a
method to determine an optimal Markov approximation for
modelling and prediction from time series data. The method
finds a balance between minimal modelling errors by taking
as much as possible memory into account and minimal
statistical errors by working in embedding spaces of rather
small dimension. A key ingredient is an estimate of the
statistical error of entropy estimates.},
note = {\arXiv{0808.1513}},
}
@MISC{LevnMezi08,
author = {Levnaji\'c, Z. and Mezi\'c, I.},
title = {Ergodic theory and visualization {I}:
{Visualization} of ergodic partition and invariant sets},
note = {\arXiv{0805.4221}},
abstract = {We present a computational study of the
invariant sets visualization method based on ergodic
partition theory. The algorithms
for computation of the time averages of many L1 functions
are developed and employed producing the approximation of
the phase space ergodic partitioning. The method is
exposed in the context of discrete-time dynamical systems
producing a graphical representation of the phase space
in terms of the invariant set structure that gives a
substantial insight into the global and local properties
of the dynamics. We use the Chirikov standard map in
order to show the implementation of the method, followed
by applications to other multi-dimensional maps. We examine
the visualization of periodic sets using harmonic time
averages.},
year = {2008},
}
@article{RoMeBaSchHe09,
author={Rowley, C. W. and Mezi\'c, I. and Bagheri, S.
and Schlatter, P. and Henningson, D. S.},
title={Spectral analysis of nonlinear flows},
journal={J. Fluid Mech.},
volume={641},
pages={115},
year = {2009},
}
@MISC{BuMoMe12,
author = {Budi{\v s}i{\'c}, M. and Mohr, R. M. and Mezi{\'c}, I.},
title = "{Applied Koopmanism}",
note = {\arXiv{1206.3164}},
year = 2012,
}
% Saraceno cites this for Ruelle-Pollicott ( RP ) resonances:
@article{ruelle86,
author = {D. Ruelle},
title = {Resonances of chaotic dynamical systems},
journal = {Phys. Rev. Lett.},
volume = {56},
abstract = {We present analytic properties of the power spectrum for
a class of chaotic dynamical systems (Axiom-A systems). The power spectrum
is meromorphic in a strip; the position of the poles (resonances) depends
on the system considered, but only their residues depend on
the observable monitored. In relation with these results we also discuss
the exponential or nonexponential decay of correlation functions at infinity.
In conclusion, it appears desirable to analyze the decay of correlation functions
and the possible analyticity of power spectra for physical time evolutions,
and for computer generated simple dynamical systems (non-Axiom-A in general).},
year = {1986},
pages = {405}
}
@ARTICLE{bog_keat,
TITLE = "Gutzwiller's trace formula and spectral statistics: beyond the diagonal approximation",
AUTHOR = "E. B. Bogomolny and J. P. Keating",
JOURNAL = "Phys. Rev. Lett.",
VOLUME = "77",
PAGES = "1472",
YEAR = "1996"
}
@ARTICLE{bog92,
TITLE = "Semiclassical quantization of multidimensional systems",
AUTHOR = "E. B. Bogomolny",
JOURNAL = "Nonlinearity",
VOLUME = "5",
PAGES = "805-866",
YEAR = "1992"
}
@ARTICLE{slg93,
TITLE = "Application of {Bogomolny} transfer operator
to semiclassical quantization of a chaotic system ",
AUTHOR = "T. Szeredi and J. H. Lefebvre and D. A. Goodings ",
JOURNAL = "Phys. Rev. Lett.",
VOLUME = "71",
PAGES = "2891--2894",
YEAR = "1993"
}
@MISC{gora05,
author = {P. F. Gora},
title = {Stationary distributions of a noisy logistic process},
note = {\arXiv{cond-mat/0502389}},
year = {2005}
}
@article{bollt06,
author = {E. Bollt and P. G\'{o}ra and A. Ostruszka and K. \.{Z}yczkowski},
title = {Basis {Markov} partitions and transition matrices for stochastic systems},
year = {2008},
journal = {SIAM J. Applied Dynam. Systems},
volume = {7},
pages = {341--360},
note = {\arXiv{nlin/0605017}},
}
@ARTICLE{BillBoll05,
author = {Billings, L. and Bollt, E. M.},
title = {
\HREF{http://people.clarkson.edu/~bolltem/Papers/csf_2001.pdf}
{``Invariant densities for skew tent maps,"}},
journal = {Chaos Solitons Fractals},
volume = {12},
pages = {365},
year = {2001},
note = {See also \weblink{www.mathstat.concordia.ca/pg/bilbollt.html}.},
}
@ARTICLE{Davidchack00,
author = {Davidchack, R.L. and Lai, Y.C. and Bollt, E.M. and Dhamala, M. },
title = {Estimating generating partitions of chaotic systems
by unstable periodic orbits},
journal = {Phys. Rev. E},
volume = {61},
pages = {1353},
year = {2000},
}
@ARTICLE{Crkov,
author = {Chirikov, B.V. },
title = {Resonance processes in magnetic traps},
journal = {At. Energ.},
volume = {6},
pages = {630},
year = {1959},
}
@ARTICLE{Plume_Lef1,
author = {Plumecoq, J. and Lefranc, M.},
title = {From template analysis to generating partitions {I}:
{Periodic} orbits, knots and symbolic encodings},
journal = {Physica D},
volume = {144},
pages = {231},
year = {2000},
}
% note ={\weblink{www.phlam.univ-lille1.fr/perso/lefranc/PDF/PhysicaD_144_231.pdf}}
@ARTICLE{Plume_Lef2,
author = {Plumecoq, J. and Lefranc, M.},
title = {From template analysis to generating partitions {II}:
{Characterization} of the symbolic encodings},
journal = {Physica D},
volume = {144},
pages = {259},
year = {2000},
}
@ARTICLE{ostruszka01,
author = {A. Ostruszka and K. Zyczkowski},
title = {Spectrum of the {Frobenius-Perron} operator for systems
with stochastic perturbation},
journal = {Phys. Lett. A},
volume = {289},
pages = {306},
note = {\arXiv{nlin/0106003}},
year = {2001}
}
@ARTICLE{GasPro95,
author = {{Gaspard}, P. and {Nicolis}, G. and Provata, A. and Tasaki, S.},
title = "{Spectral signature of the pitchfork bifurcation:
{Liouville} equation approach}",
journal = {Phys. Rev. E},
year = 1995,
volume = 51,
pages = {74-94},
}
@ARTICLE{ZhuLai03,
author = {{Zhu}, L. and {Lai}, Y.-C. and {Hoppensteadt}, F.~C. and {Bollt}, E.~M.
},
title = "{Numerical and experimental investigation of
the effect of filtering on chaotic symbolic dynamics}",
journal = {Chaos},
year = 2003,
volume = 13,
pages = {410-419},
doi = {10.1063/1.1520090},
}
@Article{Subbiah98,
author = "S. Subbiah and D. J. Driebe",
title = "Spectral decomposition of the tent map with varying
height",
journal = "Chaos",
volume = "8",
pages = "741--756",
year = "1998",
keywords = "nonlinear dynamics, tent map",
}
@Article{Driebe96,
author = "D. J. Driebe and G. E. Ordnez",
title = "Using symmetries of the {Frobenius-Perron} operator to
determine spectral decompositions",
journal = "Phys. Lett. A",
volume = "211",
pages = "204--210",
year = "1996",
keywords = "Frobenius-Perron, piecewise-linear, map",
}
@Article{Ordonez96,
author = "G. E. Ordonez and D. J. Driebe",
title = "Spectral decomposition of tent maps using symmetry
considerations",
journal = "J. Stat. Phys.",
volume = "84",
pages = "269--276",
year = "1996",
keywords = "Frobenius-Perron, coupled systems, tent map,
symmetry",
}
@Article{nlin0102039,
title = "Periodic orbit quantization of a {Hamiltonian} map on
the sphere",
author = "A. J. Scott and G. J. Milburn",
year = "2001",
volume = "34",
abstract = "In a previous paper we introduced examples of
Hamiltonian mappings with phase space structures
resembling circle packings. It was shown that a vast
number of periodic orbits can be found using special
properties. We now use this information to explore the
semiclassical quantization of one of these maps.",
journal = "J. Phys. A",
pages = "7541",
note = {\arXiv{nlin/0102039}},
}
@ARTICLE{nlin0312062,
author = {{Garc{\'{\i}}a-Mata}, I. and {Saraceno}, M.},
title = "{Spectral properties and classical decays in quantum open systems}",
journal = {Phys. Rev. E},
note = {\arXiv{nlin/0312062}},
year = 2004,
volume = 69,
pages = {056211},
}
@ARTICLE{ErSar08,
author = {Saraceno, M. and Ermann, L.},
title = "A periodic orbit basis for the quantum baker's map",
journal = {Phys. Rev. E},
year = 2008,
volume = 78,
pages = {036221 },
note = {\arXiv{0806.4590}},
}
@ARTICLE{VeSchRi08,
author = {Vergini, E. G. and D. M. Schneider and A. M. F. Rivas},
title = "The short periodic orbit approach for {Quantum Cat Maps}",
journal = {J. Phys. A},
volume = 41,
pages = {405102},
year = 2008,
}
@ARTICLE{Verg00,
author = {Vergini, E. G.},
title = "Semiclassical theory of short periodic orbits
in quantum chaos",
journal = {J. Phys. A},
volume = 33,
pages = {4709-4716},
year = 2000,
note = {\arXiv{chao-dyn/9904038}},
}
@ARTICLE{VerCar_scar,
author = {Vergini, E. G. and G. Carlo},
title = "Semiclassical construction of resonances with hyperbolic
structure: the scar function",
journal = {J. Phys. A},
volume = 34,
pages = {4525-4552},
year = 2000,
}
@ARTICLE{VerCar00,
author = {Vergini, E. G. and G. Carlo},
title = "Semiclassical quantization with short periodic orbits",
journal = {J. Phys. A},
volume = 33,
pages = {4717-4724},
year = 2000,
note = {\arXiv{chao-dyn/9904039}},
}
@misc{akesson98discrete,
author = "Akesson, F. and Lehoczky, J. P. ",
title = "Discrete eigenfunction expansion of
multi-dimensional {Brownian} motion and the
{Ornstein-Uhlenbeck} process",
note = "preprint, Math. Sciences, Carnegie Mellon Univ.",
year = "1998",
}
url = "citeseer.ist.psu.edu/akesson98discrete.html"
@Book{AbrSte64,
editor = "Abramowitz, M. and Stegun, I. A.",
title = "Handbook of Mathematical Functions",
publisher = "Dover",
address = "New York",
year = "1964",
}
@ARTICLE{BuKe05,
author = {{Buhl}, M. and {Kennel}, M.~B.},
title = "Statistically relaxing to generating partitions
for observed time-series data",
journal = {Phys. Rev. E},
year = 2005,
volume = 71,
pages = {046213},
}
@ARTICLE{BuKe03,
author = {Kennel, M. B. and Buhl, M.},
title = "Estimating good discrete partitions from observed data:
{Symbolic} false nearest neighbors",
journal = {Phys. Rev. Lett.},
note = {\arXiv{nlin/0304054}},
year = 2003,
volume = 91,
pages = {084102},
}
@INPROCEEDINGS{BuKe03a,
author = {Kennel, M. B. and Buhl, M.},
title = "Estimating good discrete partitions from observed data:
symbolic false nearest neighbors",
booktitle = {Experimental Chaos: Seventh Experimental Chaos Conference},
year = 2003,
publisher = {Am. Inst. of Phys.},
address = {Melville, New York},
editor = "Ko\v{c}arev, L. and Carroll, T. L. and Gluckman,
B. J. and Boccaletti, S. and Kurths, J.",
pages = {380--380},
}
@ARTICLE{OrnUhl30,
author = {{Uhlenbeck}, G. E. and {Ornstein}, L. S.},
title = "{On the theory of the {Brownian} motion}",
journal = {Phys. Rev.},
year = 1930,
volume = 36,
pages = {823-841},
}
@BOOK{Ulam60,
author = {{Ulam}, S.~M.},
title = {A Collection of Mathematical Problems},
publisher = {Interscience Publishers},
address = {New York},
year = 1960,
}
New York, 1960), see p. 73.
@ARTICLE{DFT03,
author = {{Daw}, C.~S. and {Finney}, C.~E.~A. and {Tracy}, E.~R.},
title = "{A review of symbolic analysis of experimental data}",
journal = {Rev. Sci. Instrum.},
year = 2003,
volume = 74,
pages = {915-930}
}
@Book{haake01,
author = {Haake, Fritz},
title = {Quantum Signatures of Chaos},
publisher = {Springer},
year = 2001,
address = {Berlin},
}
@Misc{HagJoy99,
title = "Exponentially accurate semiclassical dynamics:
propagation, localization, {E}hrenfest times, scattering
and more general states",
author = "Hagedorn, G. A. and Joye, A.",
year = "1999",
abstract = "We prove six theorems concerning exponentially
accurate semiclassical quantum mechanics. Two of these
theorems are known results, but have new proofs. Under
appropriate hypotheses, they conclude that the exact
and approximate dynamics of an initially localized wave
packet agree up to exponentially small errors in
$\hbar$ for finite times and for Ehrenfest times. Two
other theorems state that for such times the wave
packets are localized near a classical orbit up to
exponentially small errors. The fifth theorem deals
with infinite times and states an exponentially
accurate scattering result. The sixth theorem provides
extensions of the other five by allowing more general
initial conditions.",
note = {\arXiv{math-ph/9911036}},
}
@MISC{angelo-2003,
author = {R. M. Angelo and L. Sanz and K. Furuya},
title = {Ordered quantization and the {E}hrenfest time scale},
note = {\arXiv{quant-ph/0302020}}},
year = {2003},
}
@ARTICLE{kaplan98,
author = {L. Kaplan},
title = {Multiplicative semiclassical dynamics and the quantization time},
journal = {Phys. Rev. E},
volume = {58},
pages = {2983},
year = {1998}
}
@ARTICLE{kaplan-2004-70,
author = {L. Kaplan},
title = {Semiclassical accuracy in phase space for regular and chaotic dynamics},
journal = {Phys. Rev. E},
volume = {70},
pages = {026223},
note = {\arXiv{nlin/0406054}},
year = {2004}
}
@ARTICLE{kaplan-2005-72,
author = {L. Kaplan},
title = {Brownian motion model of quantization ambiguity
and universality in chaotic systems},
journal = {Phys. Rev. E},
volume = {72},
pages = {036214},
note = {\arXiv{nlin/0507046}},
year = {2005}
}
@ARTICLE{EFKKLM08,
author = {R. Estrada and S. A. Fulling and L. Kaplan
and K. Kirsten and Z. Liu and and K. A. Milton},
title = {Vacuum stress-energy density and its
gravitational implications},
journal = {J. Phys. A},
volume = {41},
pages = {164055},
year = {2008}
}
@ARTICLE{SmiKap09,
author = {Smith, A. M. and Kaplan, L.},
title = {Method to modify {Random Matrix Theory}
using short-time behavior in chaotic systems},
journal = {Phys. Rev. E},
volume = {80},
pages = {035205(R)},
note = {\arXiv{0907.5037}},
year = {2009}
}
@ARTICLE{SmiKap10,
author = {Smith, A. M. and Kaplan, L.},
title = {Integrating {Random Matrix Theory} predictions
with short-time dynamical effects in chaotic systems},
journal = {Phys. Rev. E},
volume = {82},
pages = {016214},
note = {\arXiv{1006.5733}},
year = {2010}
}
@Misc{Brouwer07,
author = {{Brouwer}, P.~W.},
title = "{Semiclassical theory of the
{E}hrenfest-time dependence of quantum transport}",
note = {\arXiv{0706.1487}},
year = 2007,
}
@ARTICLE{CamPre02,
title = "Quantum breaking time near classical equilibrium
points",
author = "F. Cametti and C. Presilla",
year = "2002",
volume = "89",
abstract = "By using numerical and semiclassical methods, we
evaluate the quantumbreaking, or Ehrenfest time for a
wave packet localized around classicalequilibrium
points of autonomous one-dimensional systems with
polynomialpotentials. We find that the Ehrenfest time
diverges logarithmically with theinverse of the Planck
constant whenever the equilibrium point is
exponentiallyunstable. For stable equilibrium points,
we have a power law divergence withexponent determined
by the degree of the potential near the equilibrium
point.",
journal = {Phys. Rev. Lett.},
pages = "040403",
note = {\arXiv{quant-ph/0201147}},
}
@Misc{CatCaf07,
author = "A. Caticha and C. Cafaro",
title = "From Information Geometry to {N}ewtonian Dynamics",
year = "2007",
note = {\arXiv{0710.1071}},
}
@article{Vasi77,
author = {Vasicek, O.},
abstract = {The paper derives a general form of the term
structure of interest rates. The following assumptions are
made: (A.1) The instantaneous (spot) interest rate follows a
diffusion process; (A.2) the price of a discount bond depends
only on the spot rate over its term; and (A.3) the market is
efficient. Under these assumptions, it is shown by means of an
arbitrage argument that the expected rate of return on any bond
in excess of the spot rate is proportional to its standard
deviation. This property is then used to derive a partial
differential equation for bond prices. The solution to that
equation is given in the form of a stochastic integral
representation. An interpretation of the bond pricing formula
is provided. The model is illustrated on a specific case.},
journal = {J. Financial Econ.},
pages = {177--188},
title = {An equilibrium characterization of the term structure},
volume = {5},
year = {1977}
}
@Article{Froy07a,
author = "G. Froyland",
title = "On {Ulam} approximation of the isolated spectrum
and eigenfunctions of hyperbolic maps",
journal = "Discrete and continuous dynamical systems",
volume = "17",
pages = "671--689",
year = "2007",
keywords = "nonlinear dynamics, transient",
}
@Article{Froy-1,
author = "G. Froyland",
title = "Computer-assisted bounds for the rate of decay of
correlation",
journal = "Commun. Math. Phys.",
volume = "189",
pages = "237--257",
year = "1997",
keywords = "nonlinear dynamics, transient",
}
@inproceedings{Froy-2,
author = "G. Froyland",
title = "Extracting dynamical behaviour via {Markov} models",
BOOKTITLE="Nonlinear Dynamics and Statistics:
Proc. Newton Inst., Cambridge 1998",
EDITOR="A. Mees",
publisher = {Birkh\"{a}user},
address = {Boston},
pages = "281--321",
year = "2001",
}
URL = "math-www.uni-paderborn.de/~froyland/froyland.ps.gz",
@ARTICLE{DellFroSer00,
author = {{Dellnitz}, M. and {Froyland}, G. and {Sertl}, S.},
title = "On the isolated spectrum of the {Perron-Frobenius} operator",
journal = {Nonlinearity},
year = 2000,
volume = 13,
pages = {1171-1188},
}
@ARTICLE{Froy99,
author = {{Froyland}, G.},
title = "Using {Ulam}'s method to calculate entropy and
other dynamical invariants",
journal = {Nonlinearity},
year = 1999,
volume = 12,
pages = {79-101},
}
@ARTICLE{FroyHD98,
author = {{Froyland}, G.},
title = "Approximating physical invariant measures of mixing
dynamical systems in higher dimensions ",
journal = {Nonlinear Analysis, Theory, Methods and Applications},
year = 1998,
volume = 32,
pages = {831-860},
}
@Article{Alfsen85,
author = "K. H. Alfsen and J. Froyland",
title = "Systematics of the {Lorenz} model at a = 10",
journal = "Phys. Scr.",
volume = "31",
pages = "15",
year = "1985",
}
@Article{Froyland83,
author = "J. Froyland",
title = "Lyapunov exponents for multidimensional orbits",
journal = "Phys. Lett. A",
volume = "97",
pages = "2",
year = "1983",
}
@Article{Froyland83a,
author = "J. Froyland",
title = "Some symmetric, two-dimensional, dissipative Maps",
journal = "Physica D",
volume = "8",
pages = "423--434",
year = "1983",
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%%%%%%%%%%%%%%%% end of Predrag's new additions %%%%%%%%%%%%%%%%%%%%%%%%%%
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immediate vicinity and that it decreases if the densityis lower}
}
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title = {Experimental Observation of Nonlinear Traveling Waves in Turbulent Pipe Flow},
journal = {Science},
volume = {305},
pages = {1594-1598},
year = {2004},
abstract = {Transition to turbulence in pipe flow is one of
the most fundamental and longest-standing problems in fluid
dynamics. Stability theory suggests that the flow remains
laminar for all flow rates, but in practice pipe flow becomes
turbulent even at moderate speeds. This transition
drastically affects the transport efficiency of mass,
momentum, and heat. On the basis of the recent discovery of
unstable traveling waves in computational studies of the
Navier-Stokes equations and ideas from dynamical systems
theory, a model for the transition process has been
suggested. We report experimental observation of these
traveling waves in pipe flow, confirming the proposed
transition scenario and suggesting that the dynamics
associated with these unstable states may indeed capture the
nature of fluid turbulence.
},
URL = {http://www.sciencemag.org/cgi/content/abstract/305/5690/1594},
eprint = {http://www.sciencemag.org/cgi/reprint/305/5690/1594.pdf}
}
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selected papers from the Eighth International
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% this extracted from ~lippolis/articles/lippolis/bibtex/lippolis.bib
%***************************************************************************
% P. Cvitanovic Aug 25 2005
% derived from ../y-lan/bibtex/nonlind.bib
************** AAAAAAAAAAA ***************************
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************** EEEEEEEEEEE ***************************
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************** FFFFFFFFFFF ***************************
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volume = {17},
pages = {315-318},
year = {1931},
}
@ARTICLE{Kurch98,
author = {J. Kurchan},
title = {Fluctuation theorem for stochastic dynamics},
journal = {J. Phys. A},
volume = {31},
pages = {3719},
year = {1998},
}
@Article{vN32,
author = "J. von Neumann",
title = "{Zur Operatorenmethode in der klassischen Mechanik}.
({German}) [{On} the operator methods of classical
mechanics]",
journal = "Ann. Math.",
volume = "33",
pages = "587--642",
year = "1932",
note = "See additions \cite{vonNeum32}. Reprinted in
\cite{Taub61}.",
}
@Article{vonNeum32,
author = "J. von Neumann",
title = "{Zus{\"a}tze zur Arbeit ``Zur Operatorenmethode in der
klassischen Mechanik''}. ({German}) [{Additions} to the
work ``{On} operator methods in classical
mechanics'']",
journal = "Ann. Math.",
volume = "33",
pages = "789--791",
year = "1932",
}
@Book{Taub61,
editor = "A. H. Taub",
title = "{John von Neumann}: Collected Works. {Volume II}:
{Operators}, Ergodic Theory and Almost Periodic
Functions in a Group",
publisher = "Pergamon Press",
address = "New York",
year = "1961",
}
% from http://www.netlib.org/bibnet/authors/v/von-neumann-john.bib
@ARTICLE{KoSch90,
author = {Kostelich, E. and Yorke, J.},
year = {1990},
title = {Noise reduction--finding the simplest dynamical
system consistent with the data},
journal = {Physica D},
volume = {41},
pages = {183--196},
}
@ARTICLE{KoSch93,
author = {Kostelich, E. and Schreiber, T.},
year = {1993},
title = {Noise reduction in chaotic time-series data: a
survey of common methods},
journal = {Phys. Rev. E},
volume = {48},
pages = {1752--1763},
}
@ARTICLE{kovalev,
author={S. Kovalevskaia},
title={Sur le probl\`eme de la rotation d'un corps solide d'un point fixe},
journal={Acta Math.},
volume={12},
pages={177},
year={1889}
}
@MISC{Kuehn11,
author = "Kuehn, C.",
title = "Deterministic continutation of stochastic metastable equilibria via
{Lyapunov} equations and ellipsoids",
note = {\arXiv{1106.3479}},
year = 2011,
}
@BOOK{kura84tur,
author = {Y. Kuramoto},
title = {Chemical Oscillations, Waves and Turbulence},
publisher = {Springer},
address = {Berlin},
year = {1984},
}
@ARTICLE{ku,
author = {Y. Kuramoto and T. Tsuzuki},
title = {Persistent propagation of concentration waves
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journal = {Progr. Theor. Phys.},
volume = {55},
pages = {365},
year = {1976},
abstract = {The KSe is derived through the CGLe near the bifurcation point. Some
scaling argument is used to sort out the domiant terms.}
}
@ARTICLE{kuturb78,
author = {Y. Kuramoto},
title = {Diffusion-Induced Chaos in Reaction Systems},
journal = {Suppl. Progr. Theor. Phys.},
volume = {64},
pages = {346-367},
year = {1978},
abstract = {Phase turbulence and amplitude turbulence are named and distinguished
from a dynamical systems point of view. The prototyped equations are derived.}
}
@ARTICLE{CK97,
AUTHOR = {O. Cepas and J. Kurchan},
TITLE = {Canonically invariant formulation of {Langevin}
and {Fokker-Planck} equations},
journal = {European Physical Journal {\bf B}},
volume = {2},
pages = {221},
year = {1998},
abstract = {
We present a canonically invariant form for the generalized Langevin
and Fokker-Planck equations. We discuss the role of constants of motion,
and the construction of conservative stochastic processes.
},
NOTE = {\arXiv{cond-mat/9706296}}
}
************** LLLLLLLLLLL ***************************
@ARTICLE{LaWe83,
title = {Asymptotic properties of general autoregressive models
and strong consistency of least-squares estimates
of their parameters},
author = {Lai, T. L. and Wei, C. Z.},
year = {1983},
journal = {J. Multivariate Analysis},
volume = {13},
pages = {1-23},
abstract = {This paper establishes several almost sure asymptotic
properties of general autoregressive processes. By
making use of these properties, we obtain a proof of
the strong consistency of the least-squares estimates
of the parameters of the process without any assumption
on the roots of the characteristic polynomial.},
}
@ARTICLE{Lalley99,
author = {Lalley, S. P.},
title = {Beneath the noise, chaos},
journal = {Ann. Statist.},
volume = {27},
year = {1999},
pages = {461--479},
}
@PhdThesis{Lan:Thesis,
author = {Y. Lan},
title = {Dynamical systems approach to 1-$d$ spatiotemporal chaos -- {A} cyclist's view},
school = {School of Physics, Geogia Institute of Technology},
year = {2004},
address = {Atlanta},
}
@ARTICLE{lanVar1,
author = {Y. Lan and P. Cvitanovi\'{c}},
title = {Variational method for finding periodic orbits in a
general flow},
journal = {Phys. Rev. E},
volume = {69},
pages = {016217},
year = {2004},
note = {\arXiv{nlin.CD/0308008}}
}
@ARTICLE{lanmaw03,
author = {Y. Lan and N. Garnier and P. Cvitanovi\'{c}},
title = {Stationary modulated-amplitude waves in the 1D complex
{G}inzburg-{L}andau equation},
journal = {Physica D},
volume = {188},
pages = {193-212},
year = {2004}
}
@Book{LaTi85,
Author = "P. Lancaster and M. Tismenetsky",
Title = "The Theory of Matrices",
publisher = {Academic Press},
address = {New York},
Year = 1985,
}
@BOOK{LM94,
AUTHOR = {A. Lasota and M. MacKey},
TITLE = {Chaos, Fractals, and Noise; Stochastic Aspects of Dynamics},
YEAR = 1994,
PUBLISHER = {Springer},
ADDRESS = {Berlin}
}
@INCOLLECTION{lauw86,
AUTHOR = {H.A. Lauwerier},
YEAR = 1986,
PAGES = {39},
EDITOR = {V. Holden},
PUBLISHER = {Princeton Univ. Press},
BOOKTITLE = {Chaos}
}
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author = {M. Lehrman and A. B. Rechester and R. B. White},
title = {Symbolic analysis of chaotic signals and turbulent fluctuations},
journal = {Phys. Rev. Lett.},
volume = {78},
pages = {54},
year = {1997},
}
@ARTICLE{Lewis84,
author={Lewis, F.},
journal={IEEE Trans. Auto. Contr.},
title={Descriptor systems: {Decomposition} into forward and backward subsystems},
year={1984},
volume={29},
pages={167--170},
}
@ARTICLE{Liao09,
author = "Liao, S. J.",
title = "On the reliability of computed chaotic solutions of
non-linear differential equations",
journal = {Tellus-A},
volume = {61},
pages = {550--564},
note = "\arXiv{0901.2986}",
year = {2009},
}
@misc{Liao11,
author = "Liao, S. J.",
title = "Chaos: a bridge from microscopic
uncertainty to macroscopic randomness",
note = "\arXiv{1108.4472}",
year = 2011,
}
@article {WaLiLi11,
author = {Wang, P. F. and Li, J. P. and Li, Q.},
title = {Computational uncertainty and the application of a
high-performance multiple precision scheme to obtaining the correct
reference solution of {Lorenz }equations},
journal = {Numerical Algorithms},
year = 2011,
}
url = {http://dx.doi.org/10.1007/s11075-011-9481-6},
@ARTICLE{LipCvi08,
author = {D. Lippolis and P. Cvitanovi\'c},
title = {How well can one resolve
the state space of a chaotic map?},
journal = {Phys. Rev. Lett.},
volume = {104},
pages = {014101},
year = {2010},
note = {\arXiv{0902.4269}},
}
@PHDTHESIS{LippolisThesis,
author = {Lippolis, D.},
title = {How well can one resolve the state space of a chaotic map?},
school = {School of Physics, Georgia Inst. of Technology},
year = {2010},
address = {Atlanta},
note = {\\\wwwcb{/projects/theses.html}}
}
@inproceedings{CviLip12,
author = {P. Cvitanovi\'c and D. Lippolis},
title = {Knowing when to stop: {How} noise frees us from determinism},
booktitle="Let's Face Chaos through Nonlinear Dynamics",
editor="M. Robnik and V. G. Romanovski",
pages = {82--126},
year="2012",
publisher = {Am. Inst. of Phys.},
address = {Melville, New York},
doi = {10.1063/1.4745574},
note = {\arXiv{1206.5506}},
}
@unpublished{LipCvi07,
author = {P. Cvitanovi\'c and D. Lippolis},
title = {Optimal resolution of the state space of a chaotic flow
in presence of noise},
note = {In preparation},
year="2012",
}
@ARTICLE{littlejohn86,
author = {Littlejohn, R. G.},
title = "The semiclassical evolution of wave packets",
journal = {Phys. Rep.},
volume = 138,
pages = {193-291},
year = 1986,
}
@ARTICLE{lorenz1,
author = {E. N. {L}orenz},
title = {Deterministic Nonperiodic Flow},
journal = {J. Atmos. Sci.},
volume = {20},
pages = {130},
year = {1963}
}
@Book{Lutk93,
author = "H. L{\"u}tkepohl",
title = "Introduction to Multiple Time Series Analysis",
publisher = "Springer-Verlag",
year = "1993",
address = "Berlin, Germany",
}
@article{Lyapunov1892,
author = {A. M. Lyapunov},
title = {The general problem of the stability of motion},
journal = {Int. J. Control},
volume = {55},
year = {1992},
pages = {531--534},
}
************** MMMMMMMMMMM ***************************
@MISC{malinin07,
author = {S. V. Malinin and V. Y. Chernyak},
title = {Classical nonlinear response of a chaotic system:
Langevin dynamics and spectral decomposition},
note = {\arXiv{nlin/0703014}},
year = {2007}
}
@ARTICLE{NLSmal91,
author = {B. A. Malomed and L. Stenflo},
title = {Modulational instabilities and soliton solutions of a generalized
nonlinear {S}chr\"{o}dinger equation},
journal = {J. Phys. A},
volume = {24},
pages = {L1149-L1153},
year = {1991},
abtract = {A Hamiltonian equation is proposed for the generalized nonlinear
Schr\"{o}dinger equation. Soliton solutions are found and the stability of the
plane waves is investigated.}
}
@ARTICLE{msr,
AUTHOR = {P. C. Martin and E. D. Siggia and H. A. Rose},
TITLE = {Statistical Mechanics of Classical Systems},
JOURNAL = {Phys. Rev. A},
YEAR = 1973,
VOLUME = 8,
NUMBER = 1,
PAGES = {423-437}
}
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AUTHOR = {G. J. Milburn},
TITLE = {Quantum and classical Liouville dynamics in the anharmonic oscillator},
JOURNAL = {Phys. Rev. A},
YEAR = 1986,
VOLUME = 33,
NUMBER = 1,
PAGES = {674-685}
}
@ARTICLE{Milb_sqa2,
AUTHOR = {G. J. Milburn and C. A. Holmes},
TITLE = {Dissipative quantum and classical Liouville dynamics in the anharmonic oscillator},
JOURNAL = {Phys. Rev. Lett.},
YEAR = 1986,
VOLUME = 56,
NUMBER = 21,
PAGES = {2237-2240}
}
@ARTICLE{Mein95s,
author = {G. Meinsma},
title = {Elementary proof of the {Routh-Hurwitz} test},
journal = {Systems and Control Letters},
volume = {25},
pages = {237--242},
year = {1995}
}
@MISC{MiFeFl08,
author = {C. Miranda-Reyes and G. Fern and J. J. Flores-Godoy},
title = {Preservation of hyperbolic equilibrium points and
synchronization in dynamical systems},
year = {2008}
}
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author = {B. Moore},
title = {Principal component analysis in linear systems:
{Controllability}, observability, and model reduction},
journal = {IEEE Trans. Automat. Contr.},
volume = {26},
year = {1981},
pages = {17--32},
}
@BOOK{Morse73,
author = {M. Morse},
title = {Variational Analysis: Critical Extremals and Sturmian Extensions},
publisher = {Wiley},
address = {New York},
year = {1973}
}
@BOOK{mosersr,
author = {J. Moser},
title = {Stable and Random Motions in Dynamical Systems},
publisher = {Princeton Univ. Press},
address = {Princeton},
year = {1973}
}
@ARTICLE{moser96,
AUTHOR = {J. Moser},
TITLE = {A rapidly converging iteration method and nonlinear partial
differential equations},
JOURNAL = {Ann. Scuola Norm. Super. Pisa},
VOLUME = {20},
PAGES = {265-315},
YEAR = 1966
}
@ARTICLE{moser96a,
AUTHOR = {J. Moser},
JOURNAL = {Ann. Scuola Norm. Super. Pisa},
VOLUME = {20},
PAGES = {499-535},
YEAR = 1966
}
************** NNNNNNNNNNN ***************************
@MISC{NeuSch97,
author = {A. Neumaier and T. Schneider},
title = {Multivariate autoregressive and {Ornstein-Uhlenbeck} processes:
{Estimates} for order, parameters, spectral information,
and confidence regions},
note = {Submitted to A.C.M. Trans. Math. Softw., unpublished},
}
@Article{NeuSch01,
author = "A. Neumaier and T. Schneider",
title = "Estimation of parameters and eigenmodes of
multivariate autoregressive models",
journal = {A.C.M. Trans. Math. Softw.},
volume = "27",
pages = "27--57",
year = "2001",
abstract = "Dynamical characteristics of a complex system can
often be inferred from analyses of a stochastic time
series model fitted to observations of the system.
Oscillations in geophysical systems, for example, are
sometimes characterized by principal oscillation
patterns, eigenmodes of estimated autoregressive (AR)
models of first order. This paper describes the
estimation of eigenmodes of AR models of arbitrary
order. AR processes of any order can be decomposed into
eigenmodes with characteristic oscillation periods,
damping times, and excitations. Estimated eigenmodes
and confidence intervals for the eigenmodes and their
oscillation periods and damping times can be computed
from estimated model parameters. As a computationally
efficient method of estimating the parameters of AR
models from high-dimensional data, a stepwise least
squares algorithm is proposed. This algorithm computes
model coefficients and evaluates criteria for the
selection of the model order stepwise for AR models of
successively decreasing order. Numerical simulations
indicate that, with the least squares algorithm, the AR
model coefficients and the eigenmodes derived from the
coefficients are estimated reliably and that the
approximate 95\% confidence intervals for the
coefficients and eigenmodes are rough approximations of
the confidence intervals inferred from the
simulations.",
}
@ARTICLE{temam85ks,
author = {B. Nicolaenko and B. Scheurer and R. Temam},
title = {Some global dynamical properties of the {K}uramoto-{S}ivashinsky
equations:nonlinear stability and attractors},
journal = {Physica D},
volume = {16},
pages = {155-183},
year = {1985}
}
@ARTICLE{NSTks85,
author = {B. Nicolaenko and B. Scheurer and R. Temam},
title = {Some global dynamical properties of the {K}uramoto-{S}ivashinsky equations:
nonlinear stability and attractors},
journal = {Physica D},
volume = {16},
pages = {155-183},
year = {1985},
abstract = {The KSe shows coherent spatial patterns but temporal chaos. The
anti-diffusion term destablizes the solutin while stability is achived by the collective
action of all modes through the nonlinear convection term. An estimate of the L^2 norm of
the solution in the antisymmetric periodic function space is given. The number of
determining Fourier modes is calculated together with fractal dimension of the strange
attractor.}
}
************** OOOOOOOOOOO ***************************
@BOOK{Oksendal03,
author = {{\O}ksendal, Bernt},
title ={Stochastic Differential Equations},
year = {2003},
publisher = {Springer},
address = {New York},
}
@article{OlGo92,
author = {Olmsted, P. D. and Goldbart, P. M.},
title = "Isotropic-nematic transition in shear flow:
{State} selection, coexistence, phase transitions, and critical behavior",
year = {1992},
pages = {4966--4993},
journal = {Phys. Rev. A},
volume = {46},
doi = {10.1103/PhysRevA.46.4966},
}
@article{OnKa79,
author = "A. Onuki and K. Kawasaki",
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{A} renormalization group approach",
journal = "Ann. Phys.",
volume = "121",
pages = "456--528",
year = "1979",
doi = "10.1016/0003-4916(79)90105-2",
}
@article{Onuki87,
author = {A. Onuki},
title = {Homogeneous block copolymer systems under shear flow},
year = {1987},
journal = {J. Chem. Phys.},
volume = {87},
pages = {3692--3697},
doi = {10.1063/1.452967}
}
@BOOK{ottbook,
author = {E. Ott},
title ={Chaos and Dynamical Systems},
publisher = {Cambridge University Press},
address = {},
year = {2002}
}
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author = {A. Ostrowski and H. Schneider},
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volume = {4},
year = {1962},
pages = {72--84},
}
@ARTICLE{OHSZKCKY04,
title = {A local ensemble {Kalman} filter for atmospheric data assimilation},
author = {Ott, E. and Hunt, B. and Szunyogh, I. and Zimin, A. and Kostelich, E.
and Corrazza, M. and Kalnay, E. and Yorke, J.},
journal = {Tellus A},
volume = {56},
year = {2004},
pages = {415--428},
}
************** PPPPPPPPPPP ***************************
@Article{PaCrFaSh80,
title = "Geometry from a Time Series",
author = {Packard, N. H. and Crutchfield, J. P. and Farmer, J. D. and Shaw, R. S.},
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volume = {45},
pages = {712--716},
year = {1980},
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title = "Models of stochastic gene expression",
author = {Paulsson, J.},
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volume = {2},
pages = {157--175},
year = {2005},
}
@Article{Pauls04,
title = "Summing up noise in gene expression",
author = {Paulsson, J.},
journal = {Nature},
volume = {427},
pages = {415--418},
year = {2004},
}
@ARTICLE{NLSper77,
author = {N. R. Pereira and L. Stenflo},
title = {Nonlinear Schr\"{o}dinger equation including growth and damping},
journal = {Phys. Fluid},
volume = {20},
pages = {1733-1734},
year = {1977},
abstract = {A nonlinear Schr\"{o}dinger equation is found with growth and damping
terms in the weakly nonlinear regime. An exact solitary solution is found for the
equation.}
}
@article{PePaVr08,
author={Petalas, Y. G. and Parsopoulos, K. E. and Vrahatis, M. N.},
title={Stochastic optimization for detecting periodic orbits
of nonlinear mappings},
volume={11},
journal={Nonlin. Phenom. Complex Sys.},
year={2008}, pages={285 -- 291}
}
@BOOK{poinper,
author = {H. Poincar\'{e}},
title ={New Methods in Celestial Mechanics},
series= {History of Modern Physics and Astronomy},
volume = {13},
publisher = {Springer},
address = {New York},
year = {1992}
}
@BOOK{poincare,
AUTHOR = {H. Poincar\'e},
TITLE = {Les m\'ethodes nouvelles de la
m\'echanique c\'eleste},
YEAR = 1899,
PUBLISHER = {Guthier-Villars},
ADDRESS = {Paris},
NOTE = {For a very readable exposition of Poincar\'e's work and
the development of the dynamical systems theory up to 1920's
see \refref{JBG97}.}
}
@BOOK{JBG97,
AUTHOR = {J. Barrow-Green},
TITLE = {Poincar\'e and the Tree Body Problem},
YEAR = 1997,
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence R.I.}
}
@book{Pontr62,
author = {Pontryagin, L. S. and V. Boltyanskii and R.
Gamkrelidge and E. Mishenko},
title = "{Mathematical Theory of Optimal Processes}",
publisher = "Interscience Publishers",
address = "New York",
year = {1962}
}
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author = "C. Preda and P. Preda",
title = "The {Lyapunov} operator equation for the exponential dichotomy
of one-parameter semigroups",
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volume = "58",
pages = "259--262",
year = "2009",
}
@Book{Press:96,
author = { W. H. Press and B. P. Flannery and S. A. Teukolsky and W. T. Vetterling},
title = {Numerical Recipes in Fortran},
publisher = {Cambridge Univ. Press},
year = {1996},
address = {Cambridge},
}
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author = {C. Pugh},
title = {An improved closing lemma and a general density theorem},
journal = {Amer. J. Math.},
volume = {89},
year = {1967}
}
************** QQQQQQQQQQQ ***************************
************** RRRRRRRRRRR ***************************
@ARTICLE{Ren57,
AUTHOR = {A. R\'nyi},
TITLE = {Representation for real numbers and their
ergodic propoerties},
JOURNAL = {Acta Math. Acad. Sci. Hungar.},
YEAR = {1957},
volume = {8},
pages = {477--493},
}
@ARTICLE{reimann1,
AUTHOR = {P. Reimann},
TITLE = {Noisy one-dimensional maps near a crisis 1: Weak
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JOURNAL = {J. Stat. Phys.},
YEAR = 1996,
VOLUME = 82,
PAGES = {1467-1501}
}
@ARTICLE{reimann2,
AUTHOR = {P. Reimann},
TITLE = {Noisy one-dimensional maps near a crisis 2: General
uncorrelated weak noise},
JOURNAL = {J. Stat. Phys.},
YEAR = 1996,
VOLUME = 85,
PAGES = {403-425}
}
@ARTICLE{AlEyRe05,
author = {Alexander, F. J. and Eyink, G. L. and Restrepo, J. M.},
title = {Accelerated {Monte Carlo}
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journal = {J. Stat. Phys.},
volume = {119},
pages = {1331--1345},
year = {2005}
}
@ARTICLE{Re08,
author = {Restrepo, J. M.},
title = {A path integral method for data assimilation},
journal = {Physica D},
volume = {237},
pages = {14--27},
year = {2008}
}
@ARTICLE{ReOtt96,
AUTHOR = {Reyl, C. and Antonsen, T.M. and Ott, E.},
TITLE = {Quasi-two-dimensional fast kinematic dynamo
instabilities of chaotic fluid flows},
JOURNAL = {Phys. Plasmas},
YEAR = {1996},
VOLUME = {3},
PAGES = {2564}
}
@BOOK{Risken96,
author = {H. Risken},
title ={The {Fokker-Planck} Equation},
publisher = {Springer},
address = {New York},
year = {1996}
}
@ARTICLE{Risken72,
author = {H. Risken},
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journal = {Z. Physik},
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pages = {251},
year = {1972},
}
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author = {Robinson, S.~K.},
title = "{Coherent motions in the turbulent boundary layer}",
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volume = 23,
pages = {601-639},
}
@ARTICLE{Ronc95,
author = {M. Roncadelli},
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pages = {4661},
year = {1995}
}
@article{DeRonc95,
author={A. Defendi and M. Roncadelli},
title={Semiclassical approximation as a small-noise expansion},
journal={J. Phys. A},
volume={28},
pages={L515-L520},
year={1995},
abstract={We discuss how the semiclassical approximation
arises within the (classically improved) Langevin
quantization. We derive a new representation of the
semiclassical propagator (at imaginary time) in the form of
a white noise average, which is valid over an arbitrary
(imaginary) time interval. Although our result is
ultimately equivalent to the standard representation of the
semiclassical propagator, it nevertheless turns out to be
more advantageous in dealing with certain problems that
involve tunnelling and metastability.}
}
@ARTICLE{ross,
author = {O. E. R\"{o}ssler},
title = {An equation for continuous chaos},
journal = {Phys. Lett. A},
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pages = {397},
year = {1976}
}
@BOOK{ruelle,
author = {D. Ruelle},
title = {Statistical Mechanics, Thermodynamic Formalism},
publisher = {Addison-Wesley},
address = {Reading, MA},
year = {1978}
}
@ARTICLE{ruell71,
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pages = {167},
year = {1971}
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@ARTICLE{Ruelle76,
author = {D. Ruelle},
title = {Zeta functions for expanding maps and {Anosov} flows},
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volume = {34},
pages = {231},
year = {1976}
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************** SSSSSSSSSSS ***************************
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% the method for calculating periodic orbits is laid out
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************** TTTTTTTTTTT ***************************
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Floquet eigenvectors in the particular case of a periodic
orbit. These vectors, called Lyapunov vectors, can be
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mechanism responsible for super-Lyapunov growth is shown to
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leading Lyapunov vectors, as defined here, as well as the
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general, point away from it. Perturbations that are on the
attractor can be found in the subspace of the leading
Lyapunov vectors.},
}
************** UUUUUUUUUUU ***************************
************** VVVVVVVVVVV ***************************
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}
************** WWWWWWWWWWW ***************************
@UNPUBLISHED{WaKo12,
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pages={475},
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volume = {59},
year = {2007},
pages = {355--366},
abstract = {
Standard techniques for computing Lyapunov vectors produce
results which are norm-dependent and lack invariance under
the linearized flow. An efficient, norm-independent method
for constructing the n most rapidly growing Lyapunov
vectors from n-1 leading forward and n leading backward
asymptotic singular vectors is proposed. The Lyapunov
vectors so constructed are invariant under the linearized
flow in the sense that, once computed at one time, they are
defined, in principle, for all time through the tangent
linear propagator. An analogous method allows the
construction of the n most rapidly decaying Lyapunov
vectors from n decaying forward and n-1 decaying backward
singular vectors.}
}
************** XXXXXXXXXXX ***************************
************** YYYYYYYYYYY ***************************
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************** ZZZZZZZZZZZ ***************************
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************** TEXTBOOKS ***************************
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%PC removed this:
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%PC removed this
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#########################
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title = {The {E}ckhaus instability for travelling waves},
journal = {Physica D},
volume = {55},
pages = {269-286},
year = {1992}
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{K}uramoto-{S}ivashinsky equation},
journal = {SIAM J. Applied Math.},
volume = {50},
pages = {760},
year = {1990}
}
@ARTICLE{pattfm,
author = {M. C. Cross and P. C. Hohenberg},
title = {Pattern formation outside of equilibrium},
journal = {Rev. Mod. Phys. },
volume = {65},
year = {1993}
}
@ARTICLE{cross94sp,
author = {M. C. Cross and P. C. Hohenberg},
title = {Spatiotemporal Chaos},
journal = {Science},
volume = {263},
pages = {1569-1570},
year = {1994},
abstract = {The phenomena of spatiotermporal chaos are introduced based on both
rotating and regular Rayleigh-Bernard convection. The enormous number of available
degrees of freedom is a vivid feature. A set of interesting questions have
been raised, including how to characterize a spatiotemporal chaotic state. The
importance of the study of small subsystems is emphasized.}
}
@ARTICLE{bknk,
author = {N. Bekki and K. Nozaki},
title = {Formations of Spatial Patterns And Holes In The Generalized
{G}inzburg-{L}andau Equation},
journal = "Phys. Lett. A"},
volume = {110},
pages = {133-135},
year = {1985}
}
@ARTICLE{bknk84,
author = {K. Nozaki and N. Bekki},
title = {Exact solutions of the generalized {G}inzburg-{L}andau equation},
journal = {J. Phys. Soc. Japan},
volume = {53},
pages = {1581-1582},
year = {1984}
}
@ARTICLE{bknk83,
author = {K. Nozaki and N. Bekki},
title = {Pattern selection and spatiotemporal transition to chaos in the
{G}inzburg-{L}andau equation},
journal = {Phys. Rev. Lett.},
volume = {51},
pages = {2171},
year = {1983}
}
@ARTICLE{BTBmaw03,
author = {L. Brusch and A. Torcini and M. B\"{a}r},
title = {Nonlinear analysis of the {E}ckhaus instability: modulated amplitude waves
and phase chaos with nonzero average phase gradient},
journal = {Physica D},
volume = {174},
pages = {152-167},
year = {2003}
}
@ARTICLE{BTHmaw01,
author = {L. Brusch and A. Torcini and M. van Hecke and M. G. Zimmermann
and M. B\"{a}r},
title = {Modulated amplitude waves and defect formation in the one-dimensional
complex {G}inzburg-{L}andau equation},
journal = {Physica D},
volume = {160},
pages = {127-148},
year = {2001}
}
@ARTICLE{BZMmaw00,
author = {L. Brusch and M. G. Zimmermann and M. van Hecke and M. B\"{a}r and
A. Torcini},
title = {Modulated amplitude waves and the transition from phase to defect chaos},
journal = {Phys. Rev. Lett.},
volume = {85},
pages = {86},
year = {2000},
abstract = {MAWs of various periods P occur in phase chaotic states. The pair of
MAWs cease to exist via a saddle-node bifurcation. For periods beyond this bifurcation,
incoherent near-MAW evolve toward defects.}
}
@ARTICLE{SHcgl90,
author = {W. van Saarloos and P. C. Hohenberg},
title = {Pulses and fronts in the complex {G}inzburg-{L}andau equation near a
subcritical bifurcation},
journal = {Phys. Rev. Lett.},
volume = {64},
pages = {749},
year = {1990}
}
@ARTICLE{SPScgl92,
author = {B. I. Shraiman and A. Pumir and W. van Saarloos
and P. C. Hohenberg and H. Chat\'{e} and M. Holen},
title = {Spatiotemporal chaos in the one-dimensional complex {G}inzburg-{L}andau
equation},
journal = {Physica D},
volume = {57},
pages = {241-248},
year = {1992}
}
@ARTICLE{MvH98,
author = {M. van Hecke},
title = {Building blocks of spatiotemporal intermittency},
journal = {Phys. Rev. Lett.},
volume = {80},
pages = {1896},
year = {1998}
}
@ARTICLE{torc96,
author = {A. Torcini},
title = {Order Parameter for the Transition from Phase to Amplitude Turbulence},
journal = {Phys. Rev. Lett.},
volume = {77},
pages = {1047},
year = {1996},
abstract = {The maximal consersed phase gradient is introduced as an order parameter
to characterize the transition from phase to defect turbulence in the CGLe. It has a
finite value in the PT regime and decreases to zero when the transition to defect
turbulence is approached. A modified KSe is able to reproduce the main feature of the
stable waves and to explain their origin.}
}
@ARTICLE{MvHhole01,
author = {M. van Hecke and M. Howard},
title = {Ordered and Self-disordered dynamics of holes and defects in the
one-dimensional complex {G}inzburg-{L}andau equation},
journal = {Phys. Rev. Lett.},
volume = {86},
pages = {2018},
year = {2001},
abtract = {Ordered hole-defect dynamics happens when an unstable hole invade a plane
wave state and periodically nucleates defects from which new holes are born. The
interaction between the holes and a self-disordered background are essential for the
occurrence of spatiotemporal chaos in hole-defect states.}
}
@ARTICLE{CM87tran,
author = {H. Chat\'{e} and P. Manneville},
title = {Transition to turbulence via spatiotemporal intermittency},
journal = {Phys. Rev. Lett.},
volume = {58},
pages = {112},
year = {1987}
}
@ARTICLE{MC96pha,
author = {P. Manneville and H. Chat\'{e}},
title = {Phase turbulence in the two-dimensional complex {G}inzburg-{L}andau equation},
journal = {Physica D},
volume = {96},
pages = {30-46},
year = {1996},
abtract = {instability of plane waves}
}
@ARTICLE{EGtran95,
author = {D. A. Egolf and H. S. Greenside},
title = {Characterization of the transition from defect to phase turbulence},
journal = {Phys. Rev. Lett.},
volume = {74},
pages = {1751},
year = {1995},
abtract = {For the CGLe on a large periodic interval, the transition from
defect to phase turbulence is continuous. The conclusion is based on the
calculation of the defect density, Lyapunov dimension density and
correlation lengths.}
}
@ARTICLE{MHMwind96,
author = {R. Montagne and E. Hern\'{a}ndez-Garc\'{i}a and M. S. Miguel},
title = {Winding number instability in the phase-turbulence regime of the complex
{G}inzburg-{L}andau equation},
journal = {Phys. Rev. Lett.},
volume = {77},
pages = {267},
year = {1996},
abstract = {There exist a band of winding numbers associated with stable states in
the phase turbulent regime. The states with large winding numbers decay to the ones
with smaller winding numbers. Defect chaos happens when the range of stable winding
numbers vanishes.}
}
@ARTICLE{Mcoh03,
author = {M. van Hecke},
title = {Coherent and incoherent structures in systems described by the {1D}
{CGLE}: {Experiments} and identification},
journal = {Physica D},
volume = {174},
pages = {134},
year = {2003},
abstract = {Give an overview of the most important properties of the coherent
structures and address the question how such structures may be identified in the
experimental space-time data set.}
}
@ARTICLE{SHcoh92,
author = {W. van Saarloos and P. C. Hohenberg},
title = {Fronts, pulses, sources and sinks in generalized complex {G}inzburg-{L}andau
equations},
journal = {Physica D},
volume = {56},
pages = {303-367},
year = {1992},
abstract = {Propose the concept of coherent structures and study the competition
between them in chaotic dynamics. Specifically, the invasion of front to another state
is discussed.}
}
@ARTICLE{TFGphase97,
author = { A. Torcini und H. Frauenkron and P. Grassberger},
title = {Studies of Phase Turbulence in the One Dimensional Complex {G}inzburg-{L}andau
Equation},
journal = {Phys. Rev. E},
volume = {55},
pages = {5073},
year = {1997},
abstract = {The phase gradient is used as an order parameter. Different states are
identified. In the PT region, a modified KSe rules the phase dynamics of the CGLe.}
}
@ARTICLE{AKcgl02,
author = {I. S. Aranson and L. Kramer},
title = {The World of the Complex {G}inzburg-{L}andau Equation},
journal = {Rev. Mod. Phys.},
volume = {74},
pages = {99-143},
year = {2002}
}
@ARTICLE{SMcgl02,
author = {J. Scheuer and B. A. Malomed},
title = {Stable and chaotic solutions of the complex {G}inzburg-{L}andau equation with
periodic boundary conditions},
journal = {Physica D},
volume = {161},
pages = {102-115},
year = {2002},
abstrac ={The behavior of the solutions of the CGLe without diffusion is studied
with a periodic boundary condition.}
}
@ARTICLE{DLBconv92,
author = {F. Daviaud and J. Lega and P. Berg\'{e} and P. Coullet and M. Dubois},
title = {Spatio-temporal intermittency in a 1D convective pattern: theoretical
model and experiments},
journal = {Physica D},
volume = {55},
pages = {287-308},
year = {1992},
abstract = {Describe the occurrence of the spatio-temporal intermittency in a 1-d
convective system that shows time-independent patterns based on the amplitude equation
approach}
}
@ARTICLE{CEEks93,
author = {P. Collet and J. -P. Eckmann and H. Epstein and J. Stubbe},
title = {Analyticity for the {K}uramoto-{S}ivashinsky equation},
journal = {Physica D},
volume = {67},
pages = {321-326},
year = {1993},
abstract = {Proved the analyticity of the solution of the KSe on a periodic interval
near the real axis and the width of the region is estimated. Numerical calculations
show that this width should not depend on the size of the interval.}
}
@ARTICLE{CEEksgl93,
author = {P. Collet and J. -P. Eckmann and H. Epstein and J. Stubbe},
title = {A global attracting set for the {K}uramoto-{S}ivashinsky equation},
journal = {Commun. Math. Phys.},
volume = {152},
pages = {203-214},
year = {1993},
abstract = {New bounds are given for the L^2 norm of solutions of the KSe (not
necessarily antisymmetric).}
}
@ARTICLE{Lega:holes,
author = {J. Lega},
title = {Traveling hole solutions of the complex Ginzburg Landau
equation: a review},
journal = {Physica D},
volume = {269},
pages = {152-153},
year = {2001}
}
@ARTICLE{temam91edd,
author = {R. Temam},
title = {Approximation of attractors, large eddy simulations and multiscale
methods},
journal = {Proc. R. Soc. Lond. A},
volume = {434},
pages = {23-39},
year = {1991},
abstract = {Estimates on the dimension of the attractors and the decay rates of
Fourier mode of NSe are given. By approximation of the inertial manifold, the
interaction between the large and small eddies are derived. Such laws open the way to
numerically efficient algorithms via multiscale mthods.}
}
@ARTICLE{spald91,
author = {D. B. Spalding},
title = {Kolmogorov's two-equation model of turbulence},
journal = {Proc. R. Soc. Lond. A},
volume = {434},
pages = {211-216},
year = {1991},
abstract = {A brief survey of modelling equations of fully developed homogeneous
turbulence. Kolmogorov's original paper is translated.}
}
@ARTICLE{kolm91,
author = {A. N. Kolmogorov},
title = {The local structure of turbulence in incompressible viscous fluid
for very large {Reynolds} numbers},
journal = {Proc. R. Soc. Lond. A},
volume = {434},
pages = {9-13},
year = {1991},
abstract = {Study the distribution of velocity difference of neighboring points
based on the locally homogeneous and locally isotropic hypothesized poperties of
turbulence motion. Two more similarity hypothesis suggested the existence of a
universal distribution for different viscosity and energy dissipation rate. The
large distance asymptotic behavior of the distribution is also deduced.}
}
@ARTICLE{FJolly95,
author = {C. Foias and M. S. Jolly},
title = {On the numerical algebraic approximation of global attractors},
journal = {Nonlinearity},
volume = {8},
pages = {295-319},
year = {1995},
abstract = {An algebraic approximation of the global attractors is developed for
the {L}orenz and KS system.}
}
@ARTICLE{HNks86,
author = {J. M. Hyman and B. Nicolaenko},
title = {The {K}uramoto-{S}ivashinsky equation: a bridge between PDE's and dynamical
systems},
journal = {Physica D},
volume = {18},
pages = {113-126},
year = {1986},
abstract = {Numerical work on the transition to chaos of the KSe. The attracting
solution manifold undergoes a complex bifurcation sequence including fixed points, limit
cycles, travelling waves, homoclinic orbits, invariant tori.}
}
@ARTICLE{HNZks86,
author = {J. M. Hyman and B. Nicolaenko and S. Zaleski},
title = {Order and complexity in the {K}uramoto-{S}ivashinsky model of weakly turbulent
interfaces},
journal = {Physica D},
volume = {23},
pages = {265-292},
year = {1986},
abstract = {The properties of the KSe is discussed in even larger domains. Still
the dynamical behavior is dominated by the skeleton of low dimensional vector fields.
More complex dynamics happens in large domain where intermittency is accurately
identified only by high-precision numerical method. The presence of strange fixed points
overrun the cellular fixed points in large scales which generates complex spatial
structure to the solutions. The Large scale statistical behavior
of the system is computed.}
}
@ARTICLE{KNSks90,
author = {I. G. Kevrekidis and B. Nicolaenko and J. C. Scovel},
title = {Back in the saddle again: a computer assisted study of the
{K}uramoto-{S}ivashinsky equation},
journal = {Siam J. Appl. Math.},
volume = {50},
pages = {760-790},
year = {1990},
abstract = {The initial bifurcations of the KSe are examined analytically and
numerically. The heteroclinic connections between symmetric solutions proved to play
an important role in the dynamics.}
}
@ARTICLE{FSTks86,
author = {U. Frisch and Z. S. She and O. Thual},
title = {Viscoelastic behavior of cellular solutions to the {K}uramoto-{S}ivashinsky
model},
journal = {J. Fluid Mech.},
volume = {168},
pages = {221-240},
year = {1986},
abstract = {The KSe on the periodic interval has stable steady states of period
2*pi/N. These "cellular" states exhibit elastic behavior under perturbations of
wavelength much longer than that of itself.}
}
@ARTICLE{AGHks88,
author = {D. Armbruster and J. Guckenheimer and P. Holmes},
title = {Heteroclinic cycles and modulated travelling waves in systems with
O(2) symmetry},
journal = {Physica D},
volume = {29},
pages = {257-282},
year = {1988},
abstract = {Consider the normal form on the center manifold for the KSe and
discuss bifurcations with intrinsic O(2) symmetry.}
}
@ARTICLE{Mks86,
author = {D. Michelson},
title = {Steady solutions of the {K}uramoto-{S}ivashinsky equation},
journal = {Physica D},
volume = {19},
pages = {89-111},
year = {1986},
abtract = {The variety of steady solution of the KSe is discussed. For large c,
there is only one odd front-like bounded solution. In decreasing c, odd solutions with
more zeros are born until finally a periodic solution is born. Associated with the
periodic solution, infinite many tori will appear in the elliptic case and Cantor-type
set of chaotic solutions, with infinite many homoclinic odd solutions.}
}
@ARTICLE{FNSTks85,
author = {C. Foias and B. Nicolaenko and G.R. Sell and R. Temam},
title = {Inertial manifold for the {K}uramoto-{S}ivashinsky equation},
journal = {C. R. Acad. Sci. I-Math},
volume = {301},
pages = {285-288},
year = {1985}
}
@ARTICLE{FNSTks88,
author = {C. Foias and B. Nicolaenko and G.R. Sell and R. Temam},
title = {Inertial manifold for the {K}uramoto-{S}ivashinsky equation and an estimate of
their lowest dimension},
journal = {J. Math. Pure Appl.},
volume = {67},
pages = {197-226},
year = {1988}
}
@ARTICLE{DHBEks96,
author = {H. Dankowicz and P. Holmes and G. Berkooz and J. Elezgaray},
title = {Local models of spatio-temporally complex fields},
journal = {Physica D},
volume = {90},
pages = {387-407},
year = {1996}
}
@ARTICLE{newenv74,
author = {A. C. Newell},
title = {Envelope equations},
journal = {Lect. Appl. Math.},
volume = {15},
pages = {157-163},
year = {1974}
}
@ARTICLE{ave99,
author = {V. M. Egu\'{i}luz and P. Alstr{\o}m
and E. Hern\'{a}ndez-Garc\'{\i}a and O. Piro},
title = {Average patterns of spatiotemporal chaos: {A} boundary effect},
journal = {Phys. Rev. E},
volume = {59},
pages = {2822},
year = {1999}
}
77777 *****
77777 Computational techniques
77777 *****
@BOOK{kellbv,
author = {H. B. Keller},
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publisher = {Dover},
address = {New York},
year = {1992}
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author = {J. W. Thomas},
title = {Numerical Partial Differential Equations},
publisher = {Spring-Verlag},
address = {New York},
year = {1995}
}
series = {Texts in Applied Mathematics},
volume = {22},
@BOOK{bl,
author = {J. Stoer and R. Bulirsch},
title = {Introduction to Numerical Analysis},
publisher = {Springer},
address = {New York},
year = {1983}
}
@BOOK{nr,
author = {W. H. Press and S. A. Teukolsky and W. T. Vetterling and
B. P. Flannery},
title = {Numerical Recipes in {C}},
publisher = {Cambridge Univ. Press},
address = {Cambridge, England},
year = {1992}
}
@BOOK{lls,
author = {B.L. Ro\v{z}destvenski\v{i} and N.N. Janenko},
title = {Systems of Quasilinear Equations and Their Applications to
Gas Dynamics},
publisher = {AMS},
address = {Providence, RI},
year = {1983}
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% series = {Translations of Mathematical Monographs},
@INCOLLECTION{brand03,
author = {A. Brandenburg},
title = {Computational aspects of astrophysical {MHD} and turbulence},
booktitle = {Advances in Nonlinear Dynamos},
editor = {A. Ferriz-Mas and M. N{\'{u}\~{n}ez}},
note = {\arXiv{astro-ph/0109497}},
publisher = {Taylor \& Francis},
address = {London},
pages ={269-344},
year = {2003}
}
series = {The Fluid Mechanics of Astrophysics and Geophysics},
volume = {9},
address = {London and New York},
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author = {H-T Kook and J. D. Meiss},
title = {Application of {N}ewton's method to {L}agrangian mappings},
journal = {Physica D},
volume = {36},
pages = {317-326},
year = {1989},
abstract = {An algorithm of {N}ewton's method is presented to find periodic
orbits for {L}agrangian mappings. The method is based on block-diagonalization
of the Hessian Matrix of the action function.}
}
@ARTICLE{mis01ks,
author = {P. Zgliczynski and K. Mischaikow},
title = {Rigorous Numerics for Partial Differential Equations: the
Kuramoto-Sivashinsky equation},
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volume = {1},
pages = {255-288},
year = {2001}
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author = {A. Varga and S. Pieters},
title = {Gradient-based approach to solve optimal periodic output
feedback control problems},
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volume = {34},
pages = {477-481},
year = {1998},
abstract = {A numerical method based on the gradient minimization and
Periodic Schur Decomposition (PSD) is devised to solve the linear-quadratic
(LQ) optimization problem the linear periodic discrete-time control systems.
It can be used as a discretized version of the similar problem in the
continuous regime.}
}
@INCOLLECTION{autod89,
author = {A. Griewank},
title = {On automatic differentiation},
booktitle = {Mathematical Programming: Recent Developments
and Applications},
editor = {M. Iri and K. Tanabe},
pages = {83-108},
publisher = {Kluwer},
address = {Amsterdam},
year = {1989}
}
@INPROCEEDINGS{carsim,
author = {C. Simo},
title = {On the analytical and numerical approximation of invariant
manifolds},
booktitle = {Les M\'{e}thodes Modernes de la M\'{e}canique C\'{e}leste
(Goutelas '89)},
editor = {D. Benest and C. Froeschl\'{e}},
pages = {285-329},
year = {1989}
}
@ARTICLE{GM00aut,
author = {J. Guckenheimer and B. Meloon},
title = {Computing periodic orbits and their bifurcations with
automatic differentiation},
journal = {SIAM J. Sci. Comp.},
volume = {22},
pages = {951 - 985},
year = {2000}
}
@ARTICLE{pimyk,
author = {H. E. Nusse and J. A. York},
title = {A procedure for finding numerical trajectories on chaotic
saddles},
journal = {Physica},
volume = {36D},
pages = {137},
year = {1989},
abstract = {{PIM} (proper interior maximum) method is proposed to find chaotic
trajectories on a nonattracting set with one-d unstable manifold. By
partitioning a straight line straddling the stable manifolds, the point with
longer and longer escaping time is found in a sequel until a sufficiently
small interval is reached when the point is considered to be very close to the
stable manifolds. After that, evolving and restraining the line element
results in a NUMERICAL orbit is obtained.}
}
@ARTICLE{pimsimp,
author = {P. Moresco and S. P. Dawson},
title = {The {PIM}-simplex method: an extension of the {PIM}-triple method
to saddles with an arbitrary number of expanding directions},
journal = {Physica},
volume = {126D},
pages = {38},
year = {1999},
abstract = {They generilized the PIM method to treat the chaotic saddle with
more than one unstable direction by introducing a simplex to cross the
stable manifolds. Combining with one method for finding local extremum in
a simplex, the authors do essentially the same job as in the simple PIM
method.}
}
@ARTICLE{pimstag,
author = {D. Sweet and H. E. Nusse. and J. A. Yorke},
title = {Stagger-and-step method: {Detecting} and computing chaotic
saddles in higher dimensions},
journal = {Phys. Rev. Lett.},
volume = {86},
pages = {2261},
year = {2001},
abstract = {This is a statistical extension of the PIM method. Here, the
representative points are selected according to the so-called Exponential
Stagger Distribution about the current point, instead of the points on the
line or vertices of a simplex. This is a brutal force method while the
authors claim that it is quite efficient.}
}
@ARTICLE{tompaid96,
author = {S. Tompaidis},
title = {Numerical study of invariant sets of a quasi-periodic
perturbation of a symplectic map},
journal = {Experimental Mathematics},
volume = {5},
pages = {211-230},
year = {1996},
abstract = {{N}ewton method is used to construct periodic orbits of longer
and longer period to approach a invariant torus with specific rotation vector.
Behavior after the break of a torus is described.}
}
@ARTICLE{StMeiss98,
author = {D. Sterling and J. D. Meiss},
title = {Computing periodic orbits using the anti-integrable limit},
journal = {Phys. Lett. A},
volume = {241},
pages = {46-52},
year = {1998},
abstract = {Singular perturbation method. Through scaling transformation,
a small parameter is introduced such that when it is equal to zero, the
map becomes simple and controlable though non-deterministic. The symbolic
dynamics is easy to build and the AI limit orbit can be extended in a unique
way to the small parameter case when the AI limit is nondegenerate. {H\'{e}non} map
is used to demonstrate the idea.}
}
@ARTICLE{aub95ant,
author = {S. Aubry},
title = {Anti-integrability in dynamical and variational problems},
journal = {Physica D},
volume = {86},
pages = {284-296},
year = {1995},
}
@ARTICLE{kev01ks,
author = {M. E. Johnson and M. S. Jolly and I. G. Kevrekidis},
title = {The {Oseberg} transition: {Visualization} of global bifurcations
for the {Kuramoto-Sivashinsky} equation},
journal = {Int. J. Bifurc. Chaos},
volume = {11},
pages = {1-18},
year = {2001}
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@ARTICLE{mart87lfa,
author = {C. C. Martens and M. J. Davis and G. S. Ezra},
title = {Local frequency analysis of chaotic motion in multidimensional
systems: {Energy} transport and bottlenecks in planar {OCS}},
journal = {Chem. Phys. Lett.},
volume = {142},
pages = {519},
year = {1987},
abstract = {local frequency analysis is used and action-angle coordinate
is parametrized by the frequency ratio. The transport zones and partial
barriers are identified according to the "noble ratio" consideration.}
}
@ARTICLE{shch04fli,
author = {E. Shchekinova and C. Chandre and Y. Lan and T. Uzer},
title = {Analyzing intramolecular dynamics by fast {Lyapunov} indicators},
journal = {J. Chem. Phys.},
volume = {121},
pages = {1-7},
year = {2004},
abstract = {Fast Lyapunov indicator method is used to identify the
chaotic and regular regions in the phase space. Periodic orbits are determined
to characterized the resonance properties of these regions.}
}
@ARTICLE{chand03tf,
author = {C. Chandre and S. Wiggins and T. Uzer},
title = {Time-frequency analysis of chaotic systems},
journal = {Physica D},
volume = {181},
pages = {171},
year = {2003},
abstract = {Use wavelets to extract local frequencies and use the major
frequencies to identify the characteristics of phase space motion.}
}
@ARTICLE{lfind,
author = {F. K. Diakonos and P. Schmelcher and O. Biham},
title = {Systematic computation of the least unstable periodic orbits in
chaotic attractors},
journal = {Phys. Rev. Lett.},
volume = {81},
pages = {4349},
year = {1998},
note = {\arXiv{chao-dyn/9810022}}
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@ARTICLE{PSDB00,
author = {D. Pingel and P. Schmelcher and F.K. Diakonos and O. Biham},
title = {Theory and applications of the systematic detection of unstable
periodic orbits in dynamical systems},
journal = {Phys. Rev. E},
volume = {62},
pages = {2119},
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%% From ~gibson/turbulence.bib
@PhdThesis{GibsonPhD,
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%%%% From FW.bib
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pages={R17-R44},
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abstract={The problem of understanding the nature of fluid
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oldest problems in fluid mechanics. So far no explanation
has been substantiated to rationalize the transition
process by which the steady unidirectional laminar flow
state gives way to a temporally and spatially disordered
three-dimensional (turbulent) solution as the flow rate
increases. Recently, new travelling wave solutions have
been discovered which are saddle points in phase space.
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of spatio-temporal periodic flow solutions which may be
used to construct a cycle expansion theory of turbulent
pipe flows. We summarize this success against the backdrop
of past work and discuss its implications for future
research. }
}
%%%%%%%%%%%%%%%%%%%% end FW.bib
%%% From JFG.bib
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% tau correction paper
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% main AHLS paper on ODE BL models
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%%%%%%%%%%%%%%%%%% end JFG.bib
%%%%% From PC.bib
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