![]() 6 jun 2004 - continuously updated: best available, but you might feel less perplexed reading the stable edition |
What's |
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individual chapters in gzipped PostScript |
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Contents |
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Index |
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Chapter 1 - Overture |
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Appendix A | |
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Chapter 2 - Flows |
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Chapter 3 - Maps |
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Chapter 4 - Local stability |
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Chapter 5 - Newtonian dynamics |
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Appendix C - Stability of Hamiltonian flows |
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Chapter 6 - Get straight |
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Chapter 7 - Cycle stability |
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Chapter 8 - Transporting densities |
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Chapter 9 - Averaging |
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Chapter 10 - Qualitative dynamics, for pedestrians |
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Appendix E: |
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Chapter 11 - Qualitative dynamics, for cyclists |
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![]() ![]() | Chapter 27 |
Semiclassical evolution
We relate the quantum propagator to the classical flow of the underlying dynamical system; the semiclassical propagator and Green's function. |
Jan 30 2002
85% finished |
![]() ![]() | Exercises | Jan 30 2002 | |
![]() | 10 Feb 2000 | ||
![]() ![]() | Chapter 28 |
Semiclassical quantization
This is what could have been done with the old quantum mechanics if physicists of 1910's were as familiar with chaos as you by now are. The Gutzwiller trace formula together with the corresponding spectral determinant, the central results of the semiclassical periodic orbit theory, are derived. |
Jan 30 2002
80% finished |
![]() ![]() | Exercises | Jan 30 2002 | |
![]() ![]() | Aug 10 2002 | ||
![]() ![]() | Chapter 26 |
Relaxation for cyclists
In Chapter 14 we offered an introductory, hands-on guide to extraction of periodic orbits by means of the Newton-Raphson method. Here we take a very different tack, drawing inspiration from variational principles of classical mechanics, and path integrals of quantum mechanics. |
Aug 30 2003
85% finished |
![]() ![]() | Exercises | Aug 30 2003 | |
![]() | 10 Feb 2000 | ||
![]() ![]() | Chapter 29 |
Chaotic scattering
Scattering off N disks, exact and semiclassical. |
12 aug 2000
80% finished |
![]() ![]() | Appendix K: | What is the meaning of traces and determinants for infinite-dimensional operators? |
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![]() ![]() | Exercises | 12 aug 2000 | |
![]() | 10 Feb 2000 | ||
![]() ![]() | Chapter 30 |
Helium atom
The helium atom spectrum computed via semiclassical spectral determinants. |
17 june 2000
96% finished |
![]() ![]() | Appendix C: | Stability of Hamiltonian flows: more details, especially for the helium. | |
![]() ![]() | Exercises | 12 aug 2000 | |
![]() ![]() | Aug 10 2002 | ||
![]() ![]() | Chapter 31 |
Diffraction distraction
Diffraction effects of scattering off wedges, eavesdropping around corners incorporated into periodic orbit theory. |
Jan 30 2002
95% finished |
![]() ![]() | Exercises | Jan 30 2002 | |
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Epilogue
Take-home problem set for the third millenium. |
6 Sept 96
10% finished |
![]() ![]() | Appendix A |
Brief history of chaos
Classical mechanics has not stood still since Newton. The formalism that we use today was developed by Euler and Lagrange. By the end of the 1800's the three problems that would lead to the notion of chaotic dynamics were already known: the three-body problem, the ergodic hypothesis, and nonlinear oscillators. |
22 Jul 97
66% finished |
![]() ![]() | Appendix B |
Infinite-dimensional flows
Flows described by partial differential equations are infinite dimensional because if one writes them down as a set of ordinary differential equations (ODEs) then one needs an infinity of the ordinary kind to represent the dynamics of one equation of the partial kind (PDE). | |
![]() ![]() | Appendix C |
Stability of Hamiltonian flows
Symplectic invariance, classical collinear helium stability worked out in detail. | |
![]() ![]() | Appendix D |
Implementing evolution
To sharpen our intuition, we outline the fluid dynamical vision, have a bout of Koopmania, and show that short-times step definition of the Koopman operator is a prescription for finite time step integration of the equations of motion. | |
![]() ![]() | Exercises | ||
![]() ![]() | Appendix E |
Symbolic dynamics techniques
Further, more advanced symbolic dynamics techniques. |
9 March 98
60% finished |
![]() ![]() | Appendix F |
Counting itineraries
Further, more advanced cycle counting techniques. | |
![]() ![]() | Exercises | ||
![]() ![]() | Appendix G |
Finding cycles
More on Newton-Raphson method. |
9 March 98
60% finished |
![]() ![]() | Appendix H |
Applications
To compute an average using cycle expansions one has to find the right eigenvalue and maybe a few of its derivatives. Here we explore how to do that for all sorts of averages, some more physical than others. | |
![]() ![]() | Exercises | ||
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![]() ![]() | Appendix I |
Discrete symmetries
Dynamical zeta functions for systems with symmetries of squares or rectangles worked out in detail. |
10 Jan 99
80% finished |
![]() ![]() | Appendix J |
Convergence of spectral determinants
A heuristic estimate of the n-th cummulant. |
12 aug 2000
30% finished |
![]() ![]() | Appendix K |
Infinite dimensional operators
What is the meaning of traces and determinants for infinite-dimensional operators? |
9 Feb 96
95% finished |
![]() ![]() | Appendix L |
Statistical mechanics recycled
The Ising-like spin systems recycled. The Feigenbaum scaling function and the Fisher droplet model. |
14 Nov 96
33% finished |
![]() ![]() | Exercises | 9 sep 98 | |
![]() | 10 Feb 2000 | ||
![]() ![]() | Appendix M |
Noise/quantum trace formulas
The quantum/noise perturbative corrections formulas derived as Bohr and Sommerfeld would have derived them were they cogniscenti of chaos, with some Vattayismo rumminations along the way. |
5 Jun 1995
50% finished |
![]() ![]() | Appendix N |
What reviewers say
Bohr, Feynman and so on turning in their graves. Ignore this. |
12 aug 2000
1% finished |
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Appendix O |
Solutions
Solutions to selected problems - often more instructive than the text itself. Recommended. |
Jan 30 2002
55% finished |
![]() ![]() | Appendix P |
Projects
The essence of this subject is incommunicable in print; the only way to developed intuition about chaotic dynamics is by computing, and you are urged to try to work through the essential steps in a project that combines the techniques learned in the course with some application of interest to you.
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12 aug 2000
55% finished |