Topological and Symbolic Dynamics

The book uses both abstract and practical approaches to explain basic and deep properties of topological and symbolic dynamics. In addition to that broad exposition, the content is also wide, as one can see from the following chapter titles: Dynamical systems (e.g., quadratic, chaotic, Feigenbaum, rotations), Topological dynamics (also entropy and ergodic systems), Symbolic dynamics, Minimal symbolic systems (including subshifts as substituitive, Sturmian, skew Sturmian, Toeplitz and others) and Cellular automata. The Appendix contains some mathematical background (compact metric spaces, topological and uniform spaces, compact groups, Perron-Frobenius theory, continuous fractions). Exercises are added to every chapter. At the end, one can find a list of 40 main theorems, a bibliography with 167 items, and both symbol and subject indexes. The book seems to be convenient both for specialists and starting mathematicians. Since the author used material from the book in his courses at several universities, the book is convenient for students as well.

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