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Synopsis
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.
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Review
"Overall the writing is clear and the author has included motivational and expository material, as well as some examples and exercises. The presentation is nicely unified, and the different parts of the book interact well."
Michael Hochman, Mathematical Reviews
Book Description
Students learning the subject from scratch will value this comprehensive text, which presents three major types of dynamics, from the basics to some of the latest results: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. It will also be a valuable reference for experienced researchers.
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- PublisherCambridge University Press
- Publication date2011
- ISBN 10 0521888859
- ISBN 13 9780521888851
- BindingHardcover
- Number of pages404
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