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Chapter 1
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Overture
C.N. Yang interview, by Kerson Huang
(Hong Kong University, July 29, 2000)
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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Trajectories
An exploration of the
Roessler attractor.
Gabor Simon, simon@nbi.dk (12 jan 2000)
1-week project:
Turbulence, and what to do about it?
in either
pdf (447 Kb) or
gzipped postscript (1.8 Mb) format.
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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Chapter 3
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Maps
Physicist's Pinball
William Benfold's
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. Prügel-Bennett's
simple pinball simulator:
overview and
c code.
(Adam: Benfold's program is superior to this one)
Three disk simulator,
A. Prügel-Bennett's
xpinball program that allows you to view orbits
and the Poincare section in the three disk billiard. Requires Unix with
X11 windows and Motif library.
Slaven Peles'
stroboscopic map for a driven pendulum,
y'' + y'/Q + sin(y) = r cos(at),
c code:
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Chapter 4
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Local stability
3-d
billiard Jacobians,
(Andreas
Wirzba, 2 Mar 95)
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Chapter 5
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Transporting densities
Niels Søndergaard, NSONDERG@nbi.dk
(30 aug 1995)
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Chapter 6
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Averaging
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Chapter 7
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Trace formulas
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Chapter 8
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Spectral determinants
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Chapter 9
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Why does it work?
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Chapter 10
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Qualitative dynamics
Donal MacKernan:
Generalized
Markov coarse graining and the observables of chaos, Ph.D. thesis
(1997).
Stadium symbolic
dynamics,
An imperfect attempt to exemplify the nontrivial aspects of Markov
diagrams, symbol planes, role of symmetry in context of a popular dynamical
systems problem. [draft, 13 April 95, 257 KB]
Periodic orbit theory:
A Study of the Rossler Attractor,
Joachim Mathiessen, joachim@fys.ku.dk
(20 jan 2000)
Hard Bunimovich
stadium, washbord diffusion
Jonas Lundbek Hansen, lundbek@kaos.nbi.dk
(23 aug 1995) - 235 KB
Soft (but
not easy) Bunimovich stadium
Sune Horlyck, HORLYCK@nbi.dk
(8 sep 1995) - 544 KB
Kai's
instructions for soft Bunimovich stadium, in Norwegian, 30 may 1995)
Sune Hørlück :
A small investigation into the Soft
Bunimovich Stadium. (may 1997)
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Chapter 11
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Counting
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Chapter 12
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Fixed points, and how to get them
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Cristel Chandre's implementation of sect. 12.3.1 "Newton method for flows", for a 2-degree of freedom
Hamiltonian flow, periodic orbits of a forced pendulum. Should be easily
adoptable to other 2-degree of freedom Hamiltonian systems, such as the collinear helium:
the overview, the
C code.
(Aug 18 2002)
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Cristel Chandre's
lecture notes for chapter 12,
"Periodic orbits: how to get them".
(Sept 2001)
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Carl P. Dettmann's
implementation of a search for periodic orbits of a flow within a Poincare
section:
"Refining periodic orbits".
(April 2002)
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A. Prügel-Bennett's program for
finding billiard periodic orbits by line minimization: the overview
is in the solutions section of chapter on fixed points, here is
C code.
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Igor Romanovsky's
implementation of
A. Prügel-Bennett's routine for finding billiard periodic orbits by line minimization,
Microsoft Fortran90 code.
- Kai T. Hansen: Alternative
method to find orbits in chaotic systems, Phys. Rev. E 52, 2388 (1995).
- F.K. Diakonos, D. Pingel and P. Schmelcher:
Systematic Detection of Unstable Periodic Orbits in Discrete
Chaotic Dynamical Systems (4 July 2000).
- Cristel
Chandre's
implementation of the cyclist relaxation methods for the
Henon and Ikeda maps
Matlab code (Dec 10 2002)
Cycle-finding
programs, F. Christiansen's numerical routines package (preliminary
version, mostly maps, 29 oct 96)
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 (preliminary
version, 29 apr 1996)
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Spatiotemporally periodic solutions by variational methods,
gzipped tar file
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Spatiotemporal
chaos in terms of unstable spatiotemporally periodic states
- Vachtang Putkaradze, putkaradze@nbi.dk
(29 apr 1996) - 190 KB
Hopf's last
hope
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Chapter 13
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Cycle expansions
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A. Prügel-Bennett's mathematica programs
to construct the the dynamical zeta function and Fredholm
determinant
overview, orbits.m, zeta.m,
fredholm.m
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P. Andrésen's
solution of problem 9.2 -
construct the dynamical zeta function and Fredholm
determinant for a logistic map repeller.
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Chapter ?
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Applications
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Chapter 14
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Why cycle?
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Chapter 15
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Thermodynamic formalism
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Chapter 17
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Discrete symmetries
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Chapter 18
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Deterministic diffusion
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Project: Deterministic diffusion, sawtooth
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Termpaper,
Peter Andresén, andresen@chaos.fys.dtu.dk
[3 Feb 99]
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Termpaper,
Christian I. Mikkelsen, cmik@fys.ku.dk
[12 Jun 99]
- Khaled A Mahdi, k-mahdi@nwu.edu
- done as
mathematica notebook, 22 Mar 1998
- Project: Deterministic diffusion, zig-zag map
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Solution
[29 sep 98]
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Termpaper,
Jakob Kisbye Dreyer, kisbye@fys.ku.dk
[3 Jun 99]
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Chapter 21
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Semiclassical evolution
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Chapter 22
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Semiclassical quantization
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Chapter 23
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Semiclassical chaotic scattering
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Chapter 24
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Helium atom
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A. Prügel-Bennett's program for
integrating helium dynamics:
overview
and
mathematica code.
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Mathematica programs for finding simple colinear helium periodic orbits:
helium_po.m contains various functions,
periodic_orbits.m illustrates how these are used
to find periodic orbits.
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The
Markov partition for collinear helium,
from
"Classical mechanics of two-electron atoms",
K. Richter, G. Tanner and D. Wintgen,
Phys. Rev.
A 48, 4182-4196 (1993).
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The
spectrum of helium obtained by periodic orbit theory
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Nikola Lars Zivkovic Schou,
nikola@fys.ku.dk
(31 jan 2000)
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Colinear
helium spectrum
- Preben Bertelsen, pbertelsen@nbi.dk
(13 Oct 1995) - 300 KB
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Helium
spectrum, s-wave model
- Kristian Schaadt, schaadt@nbi.dk
(13 Oct 1995) - 453 KB
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Lopez Castillo on
hydrogen molecule.
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Chapter 25
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Diffraction distraction
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Chapter 19
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Irrationally winding
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Chapter ??
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Border of order
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Chapter 25
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Statistical mechanics
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