Entropy in Dynamical Systems

Tomasz Downarowicz (Professor)

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English

Cambridge University Press
12 May 2011

Differential calculus & equations; Non-linear science

Series: New Mathematical Monographs

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.

By: Tomasz Downarowicz (Professor)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 18
Dimensions: Height: 235mm, Width: 160mm, Spine: 25mm
Weight: 690g
ISBN: 9780521888851
ISBN 10: 0521888859
Series: New Mathematical Monographs
Pages: 404
Publication Date: 12 May 2011
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Tomasz Downarowicz is Full Professor of Mathematics at Wroclaw University of Technology, Poland.

Reviews for Entropy in Dynamical Systems

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