Entropy in dynamical systems

"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...

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Bibliographic Details
Main Author Downarowicz, Tomasz, 1956- (Author)
Format Book
LanguageEnglish
Published Cambridge ; New York : Cambridge University Press, 2011
Edition1st pub.
SeriesNew mathematical monographs
Subjects
informační entropie
dynamické systémy
information entropy
dynamical systems
učebnice
textbooks
Online AccessObálka
ISBN9780521888851
Physical Descriptionxii, 391 s. : il. ; 24 cm

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TOC from ObalkyKnih.cz
Table of 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; List of symbols; References; Index

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