stable
version 11,
28 dec 2004;
current 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 - You might also want to read about the history of the subject. | ||
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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 (more details, especially for the helium) | ||
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Chapter 6 - Billiards |
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Chapter 7 - Get straight |
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Chapter 8 - Cycle stability |
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Chapter 9 - Transporting densities |
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Chapter 10 - Averaging |
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Chapter 11 - Qualitative dynamics, for pedestrians |
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appendix E - further, more advanced symbolic dynamics techniques. | ||
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Chapter 12 - Qualitative dynamics, for cyclists |
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Chapter 13 - Counting, for pedestrians |
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Chapter 14 - Trace formulas |
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Chapter 15 - Spectral determinants |
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Chapter 16 - Why does it work? |
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Chapter 17 - Fixed points, and how to get them |
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Chapter 18 - Cycle expansions |
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Chapter 19 - Why cycle? |
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Chapter 20 _ Thermodynamic formalism |
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Chapter 21 - Intermittency |
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Chapter 22 - Discrete symmetries |
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appendix I - further examples of discrete symmetry: rectangles and squares. | ||
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Chapter 23 - Deterministic diffusion |
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Chapter 24 - Irrationally winding |
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![]() ![]() | Chapter 28 |
Semiclassical evolution
We relate the quantum propagator to the classical flow of the underlying dynamical system; the semiclassical propagator and Green's function. |
![]() ![]() | Exercises | |
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![]() ![]() | Chapter 29 |
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. |
![]() ![]() | Exercises | |
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![]() ![]() | Chapter 30 |
Relaxation for cyclists
In Chapter 17 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. |
![]() ![]() | Exercises | |
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![]() ![]() | Chapter 31 |
Quantum scattering
Scattering off N disks, exact and semiclassical. |
![]() ![]() | Appendix K: | What is the meaning of traces and determinants for infinite-dimensional operators? |
![]() ![]() | Exercises | |
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![]() ![]() | Chapter 32 |
Helium atom
The helium atom spectrum computed via semiclassical spectral determinants. |
![]() ![]() | Appendix C: | Stability of Hamiltonian flows: more details, especially for the helium. |
![]() ![]() | Exercises | |
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![]() ![]() | Chapter 33 |
Diffraction distraction
Diffraction effects of scattering off wedges, eavesdropping around corners incorporated into periodic orbit theory. |
![]() ![]() | Exercises | |
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Epilogue
Take-home problem set for the third millenium. |
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Counting itineraries
Further, more advanced cycle counting techniques. | |
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Finding cycles
More on Newton-Raphson method. | |
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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. | |
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![]() ![]() | Appendix I |
Discrete symmetries
Dynamical zeta functions for systems with symmetries of squares or rectangles worked out in detail. | |
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Convergence of spectral determinants
A heuristic estimate of the n-th cummulant. | |
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Infinite dimensional operators
What is the meaning of traces and determinants for infinite-dimensional operators? | |
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Statistical mechanics recycled
The Ising-like spin systems recycled. The Feigenbaum scaling function and the Fisher droplet model. | |
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![]() ![]() | 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. | |
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What reviewers say
Bohr, Feynman and so on turning in their graves. Ignore this. | |
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Appendix O |
Solutions
Solutions to selected problems - often more instructive than the text itself. Recommended. |
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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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