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H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley 1994). T. D. A. 7] E. Ott, Chaos in Dynamical Systems (Cambridge Univ. Press, Cambridge 1993). 8] H. 9] For a very readable exposition of Poincar´e’s work and the development of the dynamical systems theory see J. Barrow-Green, Poincar´e and the Three Body Problem, (Amer. Math. , 1997), and F. Diacu and P. Holmes, Celestial Encounters, The Origins of Chaos and Stability (Princeton Univ. Press, Princeton NJ 1996). S. D. 11] A. Katok and B.

The dynamics of distributions of trajectories is described in terms of evolution operators. In the evolution operator formalism the dynamical averages are given by exact formulas, extracted from the spectra of evolution operators. The key tools are the trace formulas and the spectral determinants. The theory of evaluation of spectra of evolution operators presented here is based on the observation that the motion in dynamical systems of few degrees of freedom is often organized around a few fundamental cycles.

5. INFINITE-DIMENSIONAL FLOWS 45 This might suffice to get you started, but as soon as you need higher numerical accuracy, you will need something better. There are many excellent reference texts and computer programs that can help you learn how to solve differential equations numerically using sophisticated numerical tools, such as pseudo-spectral methods or implicit methods. 8 on p. 54 days and gobbles up terabits of memory, you are using brain-damaged high level software. Try writing a few lines of your own Runge-Kuta code in some mundane everyday language.

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Classical and quantum chaos book by Cvitanovic et al.


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