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BibTeX files related to the ChaosBook
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ChaosBook.bib - ChaosBook bibliography (ver. April 2020)
pipes.bib - mostly fluid dynamics (ver. April 2020)
siminos.bib - mostly symmetries in dynamics (ver. April 2020)
cardiac.bib - mostly cardiac dynamics (ver. September 2017)
lippolis.bib - mostly stochastic dynamics (ver. April 2020)
mainieri.bib - mostly dynamical systems (ver. March 2016)
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Figures used in ChaosBook
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source code available upon especially persuasive requests.
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C.N. Yang interview
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Kerson Huang
(Hong Kong University, July 29, 2000) [password needed]
A very personal and in parts hilarious
overview of the 20th century physics - should you really be reading
this
book? Click here for few quotes.
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Chapter 2
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Go with the flow |
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DynamicalSystems.jl: A Julia software library for chaos and nonlinear dynamics
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George Datseris
A Julia library that offers functionality useful in study of chaos, nonlinear dynamics and
time-series analysis (2018).
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Exercises : Numerical integration of Rössler system on
numpy
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Nazmi Burak Budanur (14 jan 2014)
Rössler system python code
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A study of the Rössler system
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Radford Mitchell, Jr. (spring 2005)
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An exploration of the Rössler attractor
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Gabor Simon (12 jan 2000)
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Periodic orbit theory:
A study of the Rössler attractor
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Joachim Mathiessen
(20 jan 2000)
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Exercises: Runge-Kutta integration, Rössler flow
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Lei Zhang
Rössler system python code
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Exercise: Classical collinear helium dynamics
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Lei Zhang
colinear helium python code
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Chapter 3
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Discrete time dynamics |
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Exercises : Rössler system Poincare sections and return map of arclengths
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Nazmi Burak Budanur (21 jan 2014)
NumPy code.
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Construction of Poincaré return maps for Rössler flow
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Arindam Basu (summer 2007)
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Stroboscopic map for a driven pendulum
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Slaven Peles
(2004)
y'' + y'/Q + sin(y) = r cos(at),
code
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Chapter 4
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Local stability |
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3-d billiard Jacobians
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Andreas Wirzba
(2 Mar 1995)
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Chapter 5
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Cycle stability |
Chapter 6
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Lyapunov exponents |
Chapter 7
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Fixed points |
Chapter 8
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Hamiltonian dynamics |
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Integrating helium dynamics
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A. Prügel-Bennett
mathematica code
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Exercise: Classical collinear helium dynamics
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Lei Zhang
colinear helium python code
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Chapter 9
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Billiards |
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DynamicalBilliards.jl: An easy-to-use, modular and extendable Julia package for Dynamical Billiard systems in two dimensions
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George Datseris
A two-dimensional (dynamical) billiard systems Julia package (2017).
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AFM trajectories
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Siddhartha Kasivajhula
Java applet which presents a stroboscopic section of a tapping mode
Atomic Force Microscope,
alongside with the (x,y) space trajectories. The program simulates
trajectoris for given initial conditions and system paramaters.
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A Python pinball simulator
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Philipp Düren
A morning spent coding a simple pinball machine in Python.
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A simple pinball simulator
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A. Prügel-Bennett
(Adam: Benfold's program is superior to this one)
c code
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Xpinball
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A. Prügel-Bennett
allows you to view orbits
and the Poincaré section in the 3-disk billiard. Requires Unix with
X11 windows and Motif library
code
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GUI matlab billiard simulator
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Mason A. Porter
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Chapter 10
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Flips, slides and turns |
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Chapter 11
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World in a mirror |
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Chapter 12
- Relativity for cyclists
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Reducing the state-space of the complex Lorenz flow
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Rebecca Wilczak
(21 aug 2009)
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Chapter 13
- Slice and Dice
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Slicing and sectioning the two-modes system to guess
its relative periodic orbits
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Nazmi Burak Budanur (27 feb 2014)
A solution set to the ChaosBook exercises for the two Fourier modes model.
Mathematica notebook
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Chapter 15
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Qualitative dynamics, for cyclists |
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Symbolic dynamics in chaotic systems
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Kai T. Hansen
(Ph.D. thesis 1993)
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Generalized Markov coarse graining and the observables of chaos
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Donal MacKernan
(Ph.D. thesis 1997)
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Symbolic Dynamics and Markov Partitions for the Stadium Billiard
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Kai T. Hansen and Predrag Cvitanović
(draft, 13 April 95)
(still a preprint:)
An imperfect attempt to exemplify the nontrivial aspects of Markov
diagrams, symbol planes, role of symmetry in context of a popular dynamical
systems problem
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Markov partition for collinear helium
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K. Richter, G. Tanner and D. Wintgen
from
"Classical mechanics of two-electron atoms",
Phys. Rev.
A 48, 4182-4196 (1993)
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Soft Bunimovich Stadium
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Sune Hørlück
(8 sep 1995)
Soft (but not easy) Bunimovich stadium: A small investigation
Kai's instructions for soft Bunimovich stadium
(in Norwegian, 30 may 1995)
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Chapter 16
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Fixed points, and how to get them |
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Periodic orbits: how to get them
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Cristel Chandre
(lecture notes, Sept 2001)
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Periodic orbits of a forced pendulum
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Cristel Chandre
(Aug 18 2002)
An implementation of sect. "Newton method for flows",
for a 2-degree of freedom Hamiltonian flow. Should be easily
adoptable to other 2-degree of freedom Hamiltonian systems,
such as the collinear helium.
c code tarball
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Construction of Poincaré return maps for Rössler flow
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Arindam Basu (summer 2007)
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Multipoint-Shooting code for periodic orbits
of the Rössler flow
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Routines that can be used to find unstable cycles in chaotic
attractors to arbitrary length if the symbolic dynamics is known.
This code is implemented for the Rössler flow, but should
be useful as an example of the method.
MPSM for Rössler.nb [mathematica]
- [pdf version]
examples of MPSM for Rössler.nb [mathematica]
cycle visualization.nb [mathematica]
Jon Newman (fall 2008)
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A topologically guided method to find orbits in chaotic systems
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Kai T. Hansen
Phys. Rev. E 52, 2388 (1995)
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Refining periodic orbits
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Carl P. Dettmann
(April 2002)
Implementation of a search for periodic orbits of a flow within a Poincaré
section
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Finding billiard periodic orbits by line minimization
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A. Prügel-Bennett
For the overview,
do chapter on fixed points exercises
c code
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Finding billiard periodic orbits by line minimization
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Igor Romanovsky
A. Prügel-Bennett's routine for finding billiard periodic orbits by line minimization
Microsoft Fortran90 code
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Finding simple colinear helium periodic orbits
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A. Prügel-Bennett
helium_po.m contains various functions
periodic_orbits.m illustrates how these are used
to find periodic orbits
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Cycle-finding programs
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F. Christiansen
(29 oct 96)
Preliminary version, mostly maps
numerical routines package
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Systematic detection of unstable periodic orbits in discrete
chaotic dynamical systems
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F.K. Diakonos, D. Pingel and P. Schmelcher
(4 July 2000)
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Routines for finding periodic orbits
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Vakhtang Putkaradze
(eternalized "preliminary version," 29 apr 1996)
Muddled instructions for using Putkaradze-Christiansen numerical
routines.
Cycle-finding programs for flows,
F. Christiansen's and V. Putkaradze's programs
for for finding periodic orbits and zeros of Fredholm determinants.
You will probably also need the sample data sets
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Chapter 18
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Counting |
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Prime orbits and prime numbers
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R. Mainieri
A quick overview of the parallels between prime numbers and prime orbits
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Chapter 19
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Transporting densities |
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Spectrum of the Liouville operator
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Niels Søndergaard
(30 aug 1995)
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Chapter 20
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Averaging |
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Periodic orbit theory of linear response, a sketch
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Predrag Cvitanović
(18 may 1998)
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Chapter 21
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Trace formulas |
Chapter 22
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Spectral determinants |
Chapter 23
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Cycle expansions |
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Dynamical zeta functions
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A. Prügel-Bennett
Mathematica programs
to construct the dynamical zeta function and Fredholm
determinant
orbits.m,
zeta.m,
fredholm.m
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A logistic map repeller
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P. Andrésen
The dynamical zeta function and Fredholm
determinant for a logistic map repeller -
solution of the chapter on cycle expansion exercise.
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Periodic orbit theory:
A study of the Rössler attractor
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Joachim Mathiessen
(20 jan 2000)
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Chapter 24
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Discrete factorization |
Chapter 25
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Why cycle? |
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Chaotic Radial Oscillations
of a Harmonically Forced Gas Bubble,
Parametric Dependence and Consequences for Sonoluminescence
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Gabor Simon
(2 feb 2000)
"Periodic orbit theory applied to a chaotically
oscillating gas bubble in water"
(with G. Simon, M.T. Levinsen, I. Csabai, Á. Horváth
and P. Cvitanović),
Nonlinearity 15, 25 (2002)
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Nonlinear dynamics of dispersion
managed breathers in Gaussian Ansatz approximation
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Rytis Paškauskas
(2 feb 2000)
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Chapter 26
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Why does it work? |
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Comparison between cycle expansion and adjoint equations
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Juri Rolf
(11 Feb 1997)
In this project J. Rolf proposed
new conjectures for an infinite family of nontrivial
spectral determinants. The results were Rolf's contribution to
``Beyond periodic orbit theory'' of
P. Cvitanović, G. Vattay, J. Rolf
and Kim Hansen,
Nonlinearity 11, 1209 (1998).
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Why does the leading eigenvalue give escape rate?
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Mario Sempf
(April 2001)
Why, again?
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Chapter 27
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Intermittency |
Chapter 28
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Deterministic diffusion |
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Deterministic diffusion, sawtooth
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Peter Andresén
(3 Feb 1999)
Termpaper
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Deterministic diffusion, sawtooth
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Christian I. Mikkelsen
(12 Jun 1999)
Termpaper
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Deterministic diffusion, sawtooth
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Khaled A Mahdi
(22 Mar 1998)
mathematica notebook termpaper
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Deterministic diffusion, zig-zag map
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Jakob Kisbye Dreyer
(3 Jun 1999)
Termpaper
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Hard Bunimovich
stadium, washbord diffusion
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Jonas Lundbek Hansen
(23 aug 1995)
Termpaper
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Introduction to chaos and diffusion
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G. Boffetta, G. Lacorata and A. Vulpiani
nlin.CD/0411023
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Chapter 29
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Turbulence? |
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Fourth-order time-stepping for stiff PDEs
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L N Trefethen
(July 2002)
(published in SIAM J. Sci. Comp.)
1-page, 1-second matlab ETDRK4 code for Kuramoto-Sivashinsky equation
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The Skeleton of Chaos
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Bruce Boghosian, 2010
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Dynamical systems approach to 1-d spatiotemporal chaos
- A cyclist's view
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Yueheng Lan
(Ph.D. thesis, Georgia Tech 2004)
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Kuramoto-Sivashinsky simulations
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Ruslan L. Davidchack
(April 2007)
A demo of the
matlab code + other source files
- improvements/additions are welcome
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Analysis and numerical experimentation,
Kuramoto-Sivashinsky system
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1-week project (April 2007)
- Kuramoto-Sivashinsky:
1. A fishing expedition;
2. Flickering flame front
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Report by spring 2007 GaTech chaos class.
"Temporary" forever:
some results not yet included (April 2007)
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Flame front: the movie
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Kirill Davydychev
(April 2007)
description
[avi format]
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Kuramoto-Sivashinsky weak turbulence
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Evangelos Siminos
(12 dec 2004)
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Turbulence, and what to do about it?
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1-week project (June 1999):
Involves analysis of
a dynamical system (fixed points, stability, bifurcations) and
numerical experimentation with integration of a set of
differential equations describing the system.
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Hopf's last hope: spatiotemporal chaos in terms of unstable recurrent patterns,
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F Christiansen, P Cvitanović and V Putkaradze
(29 apr 1996)
Nonlinearity 10, 50 (1997),
chao-dyn/9606016
Fig
1, Fig
2, Fig
3, Fig
4
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Local Structures in Extended Systems
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Vachtang Putkaradze
(Ph.D. thesis 1997)
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Chapter **
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Dimension of turbulence? |
Geometry of inertial manifolds in nonlinear dissipative dynamical systems
Xiong Ding
(Ph.D. thesis, Georgia Tech 2017)
Estimating dimension of inertial manifold from unstable periodic orbits
Xiong Ding, H. Chaté, Predrag Cvitanović, E. Siminos, and K. A. Takeuchi
arXiv:1604.01859
Periodic eigendecomposition and its application to Kuramoto-Sivashinsky system
Xiong Ding and Predrag Cvitanović
arXiv:1406.4885
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Chapter **
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Universality in transitions to chaos |
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Universality in complex discrete dynamics
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M.J. Feigenbaum
(Aug 26, 1976)
"The Second Los Alamos workshop on Mathematics in Natural Sciences,".
Los Alamos Theoretical Division Annual Report 1975-1976, pp. 98-102.
(first published report on
universality in period doubling), read more about it
here.
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Exercise: Period doubling in your pocket
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E. Greco
(Sep 19 2006)
matlab code - different steps of the solution,
matlab code - webgraph only
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Exercise: Period doubling in your pocket
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J. Millan (Sep 19 2006)
c/gnuplot code
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Chapter 30
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Irrationally winding
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Chapter 31
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Noise
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Fluctuations and Irreversible Processes
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L. Onsager and S. Machlup
Phys. Rev. 91 , 1505, 1512 (1953)
and
the sequel
[password needed]
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Itô calculus
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notes by A. Prügel-Bennett
(June 1995)
M.J. Feigenbaum course on stochastic integration
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Chapter 32
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Relaxation for cyclists
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Dynamical systems approach to 1-d spatiotemporal chaos
- A cyclist's view
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Yueheng Lan
(Ph.D. thesis, Georgia Tech 2004)
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Papers on variational periodic orbit searches
-
Y Lan and P Cvitanović
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Implementation of the cyclist relaxation methods for the
Henon and Ikeda maps
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Cristel Chandre
(Dec 10 2002)
matlab code
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Variational search for periodic orbits
- Evangelos Siminos
variational search fortran code
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Spatiotemporally periodic solutions by variational methods,
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P Cvitanović
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Systematic detection of unstable periodic orbits in discrete
chaotic dynamical systems
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F.K. Diakonos, D. Pingel and P. Schmelcher
(4 July 2000)
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