Entropy in Dynamical Systems / Tomasz Downarowicz.

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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 Genera...

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Bibliographic Details
Uniform Title:New mathematical monographs ; 18.
Main Author: Downarowicz, Tomasz, 1956- (Author)
Language:English
Published: Cambridge : Cambridge University Press, 2011.
Series:New mathematical monographs ; 18.
Subjects:
Topological entropy > Textbooks.
Topological dynamics > Textbooks.
Genre:
Textbooks.
Online Access:
Connect to online resource - MSU authorized users (Digital Object Identifier Permalink)
Physical Description:1 online resource (xii, 391 pages) : digital, PDF file(s).
Format: Electronic eBook
Contents:
  • Introduction
  • Part I. Entropy in Ergodic Theory: 1. Shannon information and entropy; 2. Dynamical entropy of a process; 3. Entropy theorems in processes; 4. Kolmogorov-Sinai entropy; 5. The Ergodic Law of Series
  • Part II. Entropy in Topological Dynamics: 6. Topological entropy; 7. Dynamics in dimension zero; 8. The entropy structure; 9. Symbolic extensions; 10. A touch of smooth dynamics
  • Part III. Entropy Theory for Operators: 11. Measure-theoretic entropy of stochastic operators; 12. Topological entropy of a Markov operator; 13. Open problems in operator entropy
  • Appendix A. Toolbox
  • Appendix B. Conditional S-M-B.