

BibTeX files related to the ChaosBook

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)


Figures used in ChaosBook

source code available upon especially persuasive requests.



C.N. Yang interview

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.

Chapter 2

Go with the flow 

DynamicalSystems.jl: A Julia software library for chaos and nonlinear dynamics

George Datseris
A Julia library that offers functionality useful in study of chaos, nonlinear dynamics and
timeseries analysis (2018).

Exercises : Numerical integration of Rössler system on
numpy

Nazmi Burak Budanur (14 jan 2014)
Rössler system python code

A study of the Rössler system

Radford Mitchell, Jr. (spring 2005)

An exploration of the Rössler attractor

Gabor Simon (12 jan 2000)

Periodic orbit theory:
A study of the Rössler attractor

Joachim Mathiessen
(20 jan 2000)

Exercises: RungeKutta integration, Rössler flow

Lei Zhang
Rössler system python code

Exercise: Classical collinear helium dynamics

Lei Zhang
colinear helium python code

Chapter 3

Discrete time dynamics 

Exercises : Rössler system Poincare sections and return map of arclengths

Nazmi Burak Budanur (21 jan 2014)
NumPy code.

Construction of Poincaré return maps for Rössler flow

Arindam Basu (summer 2007)

Stroboscopic map for a driven pendulum

Slaven Peles
(2004)
y'' + y'/Q + sin(y) = r cos(at),
code

Chapter 4

Local stability 

3d billiard Jacobians

Andreas Wirzba
(2 Mar 1995)

Chapter 5

Cycle stability 
Chapter 6

Lyapunov exponents 
Chapter 7

Fixed points 
Chapter 8

Hamiltonian dynamics 

Integrating helium dynamics

A. PrügelBennett
mathematica code

Exercise: Classical collinear helium dynamics

Lei Zhang
colinear helium python code

Chapter 9

Billiards 

DynamicalBilliards.jl: An easytouse, modular and extendable Julia package for Dynamical Billiard systems in two dimensions

George Datseris
A twodimensional (dynamical) billiard systems Julia package (2017).

AFM trajectories

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.

A Python pinball simulator

Philipp Düren
A morning spent coding a simple pinball machine in Python.

A simple pinball simulator

A. PrügelBennett
(Adam: Benfold's program is superior to this one)
c code

Xpinball

A. PrügelBennett
allows you to view orbits
and the Poincaré section in the 3disk billiard. Requires Unix with
X11 windows and Motif library
code

GUI matlab billiard simulator

Mason A. Porter

Chapter 10

Flips, slides and turns 

Chapter 11

World in a mirror 

Chapter 12
 Relativity for cyclists


Reducing the statespace of the complex Lorenz flow

Rebecca Wilczak
(21 aug 2009)

Chapter 13
 Slice and Dice


Slicing and sectioning the twomodes system to guess
its relative periodic orbits

Nazmi Burak Budanur (27 feb 2014)
A solution set to the ChaosBook exercises for the two Fourier modes model.
Mathematica notebook


Chapter 15

Qualitative dynamics, for cyclists 

Symbolic dynamics in chaotic systems

Kai T. Hansen
(Ph.D. thesis 1993)

Generalized Markov coarse graining and the observables of chaos

Donal MacKernan
(Ph.D. thesis 1997)

Symbolic Dynamics and Markov Partitions for the Stadium Billiard

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

Markov partition for collinear helium

K. Richter, G. Tanner and D. Wintgen
from
"Classical mechanics of twoelectron atoms",
Phys. Rev.
A 48, 41824196 (1993)

Soft Bunimovich Stadium

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)

Chapter 16

Fixed points, and how to get them 

Periodic orbits: how to get them

Cristel Chandre
(lecture notes, Sept 2001)

Periodic orbits of a forced pendulum

Cristel Chandre
(Aug 18 2002)
An implementation of sect. "Newton method for flows",
for a 2degree of freedom Hamiltonian flow. Should be easily
adoptable to other 2degree of freedom Hamiltonian systems,
such as the collinear helium.
c code tarball

Construction of Poincaré return maps for Rössler flow

Arindam Basu (summer 2007)

MultipointShooting code for periodic orbits
of the Rössler flow

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)

A topologically guided method to find orbits in chaotic systems

Kai T. Hansen
Phys. Rev. E 52, 2388 (1995)

Refining periodic orbits

Carl P. Dettmann
(April 2002)
Implementation of a search for periodic orbits of a flow within a Poincaré
section

Finding billiard periodic orbits by line minimization

A. PrügelBennett
For the overview,
do chapter on fixed points exercises
c code

Finding billiard periodic orbits by line minimization

Igor Romanovsky
A. PrügelBennett's routine for finding billiard periodic orbits by line minimization
Microsoft Fortran90 code

Finding simple colinear helium periodic orbits

A. PrügelBennett
helium_po.m contains various functions
periodic_orbits.m illustrates how these are used
to find periodic orbits

Cyclefinding programs

F. Christiansen
(29 oct 96)
Preliminary version, mostly maps
numerical routines package

Systematic detection of unstable periodic orbits in discrete
chaotic dynamical systems

F.K. Diakonos, D. Pingel and P. Schmelcher
(4 July 2000)

Routines for finding periodic orbits

Vakhtang Putkaradze
(eternalized "preliminary version," 29 apr 1996)
Muddled instructions for using PutkaradzeChristiansen numerical
routines.
Cyclefinding 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


Chapter 18

Counting 

Prime orbits and prime numbers

R. Mainieri
A quick overview of the parallels between prime numbers and prime orbits

Chapter 19

Transporting densities 

Spectrum of the Liouville operator

Niels Søndergaard
(30 aug 1995)

Chapter 20

Averaging 

Periodic orbit theory of linear response, a sketch

Predrag Cvitanović
(18 may 1998)

Chapter 21

Trace formulas 
Chapter 22

Spectral determinants 
Chapter 23

Cycle expansions 

Dynamical zeta functions

A. PrügelBennett
Mathematica programs
to construct the dynamical zeta function and Fredholm
determinant
orbits.m,
zeta.m,
fredholm.m

A logistic map repeller

P. Andrésen
The dynamical zeta function and Fredholm
determinant for a logistic map repeller 
solution of the chapter on cycle expansion exercise.

Periodic orbit theory:
A study of the Rössler attractor

Joachim Mathiessen
(20 jan 2000)

Chapter 24

Discrete factorization 
Chapter 25

Why cycle? 

Chaotic Radial Oscillations
of a Harmonically Forced Gas Bubble,
Parametric Dependence and Consequences for Sonoluminescence

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)

Nonlinear dynamics of dispersion
managed breathers in Gaussian Ansatz approximation

Rytis Paškauskas
(2 feb 2000)

Chapter 26

Why does it work? 

Comparison between cycle expansion and adjoint equations

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).

Why does the leading eigenvalue give escape rate?

Mario Sempf
(April 2001)
Why, again?

Chapter 27

Intermittency 
Chapter 28

Deterministic diffusion 

Deterministic diffusion, sawtooth

Peter Andresén
(3 Feb 1999)
Termpaper

Deterministic diffusion, sawtooth

Christian I. Mikkelsen
(12 Jun 1999)
Termpaper

Deterministic diffusion, sawtooth

Khaled A Mahdi
(22 Mar 1998)
mathematica notebook termpaper

Deterministic diffusion, zigzag map

Jakob Kisbye Dreyer
(3 Jun 1999)
Termpaper

Hard Bunimovich
stadium, washbord diffusion

Jonas Lundbek Hansen
(23 aug 1995)
Termpaper

Introduction to chaos and diffusion

G. Boffetta, G. Lacorata and A. Vulpiani
nlin.CD/0411023

Chapter 29

Turbulence? 

Fourthorder timestepping for stiff PDEs

L N Trefethen
(July 2002)
(published in SIAM J. Sci. Comp.)
1page, 1second matlab ETDRK4 code for KuramotoSivashinsky equation

The Skeleton of Chaos

Bruce Boghosian, 2010

Dynamical systems approach to 1d spatiotemporal chaos
 A cyclist's view

Yueheng Lan
(Ph.D. thesis, Georgia Tech 2004)

KuramotoSivashinsky simulations

Ruslan L. Davidchack
(April 2007)
A demo of the
matlab code + other source files
 improvements/additions are welcome

Analysis and numerical experimentation,
KuramotoSivashinsky system

1week project (April 2007)
 KuramotoSivashinsky:
1. A fishing expedition;
2. Flickering flame front

Report by spring 2007 GaTech chaos class.
"Temporary" forever:
some results not yet included (April 2007)

Flame front: the movie

Kirill Davydychev
(April 2007)
description
[avi format]

KuramotoSivashinsky weak turbulence

Evangelos Siminos
(12 dec 2004)

Turbulence, and what to do about it?

1week 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.

Hopf's last hope: spatiotemporal chaos in terms of unstable recurrent patterns,

F Christiansen, P Cvitanović and V Putkaradze
(29 apr 1996)
Nonlinearity 10, 50 (1997),
chaodyn/9606016
Fig
1, Fig
2, Fig
3, Fig
4

Local Structures in Extended Systems

Vachtang Putkaradze
(Ph.D. thesis 1997)

Chapter **

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 KuramotoSivashinsky system
Xiong Ding and Predrag Cvitanović
arXiv:1406.4885

Chapter **

Universality in transitions to chaos 

Universality in complex discrete dynamics

M.J. Feigenbaum
(Aug 26, 1976)
"The Second Los Alamos workshop on Mathematics in Natural Sciences,".
Los Alamos Theoretical Division Annual Report 19751976, pp. 98102.
(first published report on
universality in period doubling), read more about it
here.

Exercise: Period doubling in your pocket

E. Greco
(Sep 19 2006)
matlab code  different steps of the solution,
matlab code  webgraph only

Exercise: Period doubling in your pocket

J. Millan (Sep 19 2006)
c/gnuplot code

Chapter 30

Irrationally winding

Chapter 31

Noise


Fluctuations and Irreversible Processes

L. Onsager and S. Machlup
Phys. Rev. 91 , 1505, 1512 (1953)
and
the sequel
[password needed]

Itô calculus

notes by A. PrügelBennett
(June 1995)
M.J. Feigenbaum course on stochastic integration

Chapter 32

Relaxation for cyclists


Dynamical systems approach to 1d spatiotemporal chaos
 A cyclist's view

Yueheng Lan
(Ph.D. thesis, Georgia Tech 2004)

Papers on variational periodic orbit searches

Y Lan and P Cvitanović

Implementation of the cyclist relaxation methods for the
Henon and Ikeda maps

Cristel Chandre
(Dec 10 2002)
matlab code

Variational search for periodic orbits
 Evangelos Siminos
variational search fortran code

Spatiotemporally periodic solutions by variational methods,

P Cvitanović

Systematic detection of unstable periodic orbits in discrete
chaotic dynamical systems

F.K. Diakonos, D. Pingel and P. Schmelcher
(4 July 2000)
