Entropy in Dynamical Systems (New Mathematical Monographs #18) (Hardcover)

Entropy in Dynamical Systems (New Mathematical Monographs #18) By Tomasz Downarowicz Cover Image

Entropy in Dynamical Systems (New Mathematical Monographs #18) (Hardcover)

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This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon-McMillan-Breiman Theorem, the Ornstein-Weiss Return Time Theorem, the Krieger Generator Theorem and, among the newest developments, the ergodic law of series. In Part II, after an expanded exposition of classical topological entropy, the book addresses Symbolic Extension Entropy. It offers deep insight into the theory of entropy structure and explains the role of zero-dimensional dynamics as a bridge between measurable and topological dynamics. Part III explains how both measure-theoretic and topological entropy can be extended to operators on relevant function spaces. Intuitive explanations, examples, exercises and open problems make this an ideal text for a graduate course on entropy theory. More experienced researchers can also find inspiration for further research.
Product Details ISBN: 9780521888851
ISBN-10: 0521888859
Publisher: Cambridge University Press
Publication Date: May 12th, 2011
Pages: 404
Language: English
Series: New Mathematical Monographs