Entropy in Dynamical Systems Tomasz Downarowicz
Series: New mathematical monographsPublication details: Cambridge New York Cambridge University Press 2011Description: xii, 391 pages ill. 24 cmISBN:- 9780521888851 (hardback)
- 0521888859 (hardback)
- 515.39
Item type | Current library | Call number | Copy number | Status | Date due | Barcode | |
---|---|---|---|---|---|---|---|
Carti | IMAR | II 36958 (Browse shelf(Opens below)) | 1 | Checked out | 04/18/2025 | 0030272 |
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II 36955 An outline of ergodic theory | II 36956 Complexity and cryptography: An introduction | II 36957 Dynamical systems and ergodic theory | II 36958 Entropy in Dynamical Systems | II 36959 Equilibrium states in ergodic theory | II 36960 The ergodic theory of discrete groups | II 36962 Geometry of sets and measures in euclidean spaces |
ENG
Cuprinde Bibliografie si Anexe
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
"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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