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June 27 2008
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Contents 

Index 

Chapter 1  Overture 

appendix A  You might also want to read about the history of the subject.  
Chapter 2  Flows 

Chapter 3  Maps 

Chapter 4  Local stability 

Chapter 5  Newtonian dynamics 

appendix C  Stability of Hamiltonian flows (more details, especially for the helium)  
Chapter 6  Billiards 

Chapter 7  Get straight 

Chapter 8  Cycle stability 

Chapter 9  Transporting densities 

Chapter 10  Averaging 

Chapter 11  Qualitative dynamics, for pedestrians 

appendix E  further, more advanced symbolic dynamics techniques.  
Chapter 12  Qualitative dynamics, for cyclists 

Chapter 13  Counting, for pedestrians 

Chapter 14  Trace formulas 

Chapter 15  Spectral determinants 

Chapter 16  Why does it work? 

Chapter 17  Fixed points, and how to get them 

Chapter 18  Cycle expansions 

Chapter 19  Why cycle? 

Chapter 20 _ Thermodynamic formalism 

Chapter 21  Intermittency 

Chapter 22  Discrete symmetries 

appendix I  further examples of discrete symmetry: rectangles and squares.  
Chapter 23  Deterministic diffusion 

Chapter 24  Turbulence? 

Chapter 25  Irrationally winding 

Chapter 25  Overture 

Chapter 26  Quantum mechanics, briefly 

Chapter 27  WKB quantization 

Chapter 28  Semiclassical evolution 

Chapter 29  Noise 

Chapter 30  Semiclassical quantization 

Chapter 31  Relaxation for cyclists 

Chapter 32  Quantum scattering 

appendix K  Traces and determinants for infinitedimensional operators?  
Chapter 33  Chaotic multiscattering 

Chapter 34  Helium atom 

appendix C  Stability of Hamiltonian flows, details for the helium  
Chapter 35  Diffraction distraction 

Epilogue 
Appendix F 
Counting itineraries
Further, more advanced cycle counting techniques.  
Exercises  
Appendix G 
Finding cycles
More on NewtonRaphson method.  
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  
Appendix I 
Discrete symmetries
Dynamical zeta functions for systems with symmetries of squares or rectangles worked out in detail.  
Appendix J 
Convergence of spectral determinants
A heuristic estimate of the nth cummulant.  
Appendix K 
Infinite dimensional operators
What is the meaning of traces and determinants for infinitedimensional operators?  
Appendix L 
Statistical mechanics recycled
The Isinglike spin systems recycled. The Feigenbaum scaling function and the Fisher droplet model.  
Exercises  
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.  
Appendix N 
Solutions
Solutions to selected problems  often more instructive than the text itself. Recommended. 

Appendix O 
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.
