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By P. Civitanovic

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Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Springer Lecture Notes in Math. 470 (1975). G. Sinai, “Gibbs measures in ergodic theory”, Russ. Math. Surveys 166, 21 (1972). G. Sinai, “Construction of Markov partitions”, Funkts. Analiz i Ego Pril. 2, 70 (1968). English translation: Functional Anal. Appl. 2, 245 (1968). 20] D. Ruelle, Statistical Mechanics, Thermodynamic Formalism, (AddisonWesley, Reading MA, 1978). 21] D. Ruelle, “Functional determinants related to dynamical systems and the thermodynamic formalism”, preprint IHES/P/95/30 (March 1995).

Mainieri, P. A. Spiegel) We start out with a recapitulation of the basic notions of dynamics. Our aim is narrow; we keep the exposition focused on prerequisites to the applications to be developed in this text. We assume that the reader is familiar with dynamics on the level of the introductory texts mentioned in sect. 8, and concentrate here on developing intuition about what a dynamical system can do. It will be a coarse brush sketch - a full description of all possible behaviors of dynamical systems is beyond human ken.

An introductory course should give students skills in qualitative and numerical analysis of dynamical systems for short times (trajectories, fixed points, bifurcations) and familiarize them with Cantor sets and symbolic dynamics for chaotic systems. 9]. 11] also emphasize hands-on approach to dynamics. With this, and a graduate level-exposure to statistical mechanics, partial differential equations and quantum mechanics, the stage is set for any of the one-semester advanced courses based on ChaosBook.

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