CHAOS: CLASSICAL AND QUANTUM - EXTRAS

HMV

program packages:
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check contents with ``unzip -l *.zip'', or ``tar tvf *.tar''
move them to desired subdirectory, extract with ``unzip *.zip'' or ``tar xvf *.tar''



Source code

BibTeX files related to the ChaosBook
ChaosBook.bib - ChaosBook bibliography (ver. March 2016)
pipes.bib - mostly fluid dynamics (ver. March 2016)
siminos.bib - mostly symmetries in dynamics (ver. March 2016)
cardiac.bib - mostly cardiac dynamics (ver. March 2016)
lippolis.bib - mostly stochastic dynamics (ver. March 2016)
mainieri.bib - mostly dynamical systems (ver. March 2016)
Figures used in ChaosBook
source code available upon especially persuasive requests.

Chapter 1 - Overture

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

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: Runge-Kutta 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

3-d 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. Prügel-Bennett
  mathematica code
Exercise: Classical collinear helium dynamics
Lei Zhang
  colinear helium python code

Chapter 9 - Billiards

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.
Physicist's Pinball
William Benfold
Java applet which presents a Poincaré section of the system, alongside the three discs. The program finds cycles with a desired itinerary and computes the escape rates.
A Python pinball simulator
Philipp Düren
A morning spent coding a simple pinball machine in Python.
A simple pinball simulator
A. Prügel-Bennett
(Adam: Benfold's program is superior to this one)
  c code
Xpinball
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
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 state-space of the complex Lorenz flow
Rebecca Wilczak (21 aug 2009)

Chapter 13 - Slice and Dice

Slicing and sectioning the two-modes system to guess its relative periodic orbits
Nazmi Burak Budanur (27 feb 2014)
A solution set to the ChaosBook exerices for the two Fourier modes model.
Mathematica notebook

Chapter 14 - Charting the state space

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 two-electron atoms", Phys. Rev. A 48, 4182-4196 (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 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
Construction of Poincaré return maps for Rössler flow
Arindam Basu (summer 2007)
Multipoint-Shooting 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. Prügel-Bennett
For the overview, do chapter on fixed points exercises
  c code
Finding billiard periodic orbits by line minimization
Igor Romanovsky
A. Prügel-Bennett's routine for finding billiard periodic orbits by line minimization
  Microsoft Fortran90 code
Finding simple colinear helium periodic orbits
A. Prügel-Bennett
  helium_po.m contains various functions
  periodic_orbits.m illustrates how these are used to find periodic orbits
Cycle-finding 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 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

Chapter 17 - Walkabout: Transition graphs

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. Prügel-Bennett
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, zig-zag 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?

Fourth-order time-stepping for stiff PDEs
L N Trefethen (July 2002)
(published in SIAM J. Sci. Comp.)
  1-page, 1-second matlab ETDRK4 code for Kuramoto-Sivashinsky equation
The Skeleton of Chaos
Bruce Boghosian, 2010
Dynamical systems approach to 1-d spatiotemporal chaos - A cyclist's view
Yueheng Lan (Ph.D. thesis, Georgia Tech 2004)
Kuramoto-Sivashinsky simulations
Ruslan L. Davidchack (April 2007)
  A demo of the matlab code + other source files - improvements/additions are welcome
Analysis and numerical experimentation, Kuramoto-Sivashinsky system
1-week project (April 2007)
Kuramoto-Sivashinsky: 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]
Kuramoto-Sivashinsky weak turbulence
Evangelos Siminos (12 dec 2004)
Turbulence, and what to do about it?
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.
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), chao-dyn/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 Kuramoto-Sivashinsky 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 1975-1976, pp. 98-102.
(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. Prügel-Bennett (June 1995)
M.J. Feigenbaum course on stochastic integration

Chapter 32 - Relaxation for cyclists

Dynamical systems approach to 1-d 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)

Chapter 33 - Quantum chaos, prologue

Chapter 34 - Quantum mechanics the short short version

Chapter 35 - WKB quantization

Chapter 36 - Semiclassical evolution

The Correspondence Principle in the Statistical Interpretation of Quantum Mechanics,
J. H. van Vleck
Proc. Natl. Acad. Sci. 14 , 178 (1928). [password]
Quantum fluids and classical determinants
P. Cvitanović, G. Vattay and A. Wirzba (13 Sept 1997)
chao-dyn/9608012
Comparing different ways of using classical dynamics information to derive quantum mechanical properties.
Wave chaos
P Cvitanović
Periodic orbit theory applied to acoustics
Niels Søndergaard
(Master's thesis, 1996)

Chapter 37 - Semiclassical quantization

Periodic orbit theory beyond semiclassics: convergence, diffraction and h-bar corrections
Per Rosenqvist
(Ph.D. thesis 1995)
A force from nothing into nothing: Casimir interactions
Andreas Wirzba
(overheads, 2003)
The diagonal approximation and beyond - Case study: the spectral two-point function
Kim Splittorf (20 Jan 2000)

Chapter 38 - Quantum scattering

Lower Limit for the Energy Derivative of the Scattering Phase Shift
the original E.P. Wigner paper (1955) [password]
Lifetime Matrix in Collision Theory
the original Smith extension of the Wigner delay (1960) [password]

Chapter 39 - Chaotic multiscattering

Quantum Mechanics and Semiclassics of Hyperbolic n-Disk Scattering Systems
Andreas Wirzba (1997)
Habilitationsschrift
4-disk resonances
Sune Fallgaard Nielsen (20 Jan 1997)

Chapter 40 - Helium atom

The spectrum of helium obtained by periodic orbit theory
Nikola Lars Zivkovic Schou (31 jan 2000)
Colinear helium spectrum
Preben Bertelsen (13 Oct 1995)
Helium spectrum, s-wave model
Kristian Schaadt (13 Oct 1995)
Dissociation of hydrogen in external magnetic field
Kasper Juel Eriksen (3 Mar 1997)
  mathematica input files
On hydrogen molecule
Lopez Castillo

Chapter 41 - Diffraction distraction

Epilogue

-

Appendix L - Thermodynamic formalism

Appendix M - Statistical mechanics recycled

Lyapunov exponent for products of random matrices
Jakob Langgaard Nielsen (6 Feb 1997)

Appendix O - Projects

Open projects
A few suggestions for possible projects. For inspiration, see also the published projects and projects homepage.