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Entropy in dynamical systems
Údaje o názvu Entropy in dynamical systems / Tomasz Downarowicz Osobní jméno Downarowicz, Tomasz, 1956- (autor) Údaje o vydání First published Nakladatel New York : Cambridge University Press, 2011 Fyz.popis xii, 391 stran : schémata ISBN 978-0-521-88885-1 (vázáno) Edice New mathematical monographs ; 18 Poznámky o skryté bibliografii a rejstřících Obsahuje bibliografii a rejstříky Poznámka o obsahu 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 Předmět.hesla entropie entropy * topologie topology * dynamické systémy dynamical systems * teorie řízení control theory * diferenciální rovnice differential equations * integrální rovnice integral equations * dynamické systémy dynamical systems Forma, žánr učebnice vysokých škol textbooks (higher) Konspekt 519.1/.8 - Kombinatorika. Teorie grafů. Matematická statistika. Operační výzkum. Matematické modelování 37.016 - Učební osnovy. Vyučovací předměty. Učebnice MDT 536.75 , 515.1 , 517.938 , 531.3 , 519.876 , 519.71 , 517.9 , 517.968 , (075.8) Země vyd. Spojené státy americké Jazyk dok. angličtina Druh dok. Knihy URL http://assets.cambridge.org/97805218/88851/cover/9780521888851.jpg Signatura Čár.kód Lokace Dislokace Info M1/3787 (PřF) 3134048444 PřF PřF, KMA – RNDr. Hron pouze prezenčně
"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"-- Anotace od vydavatele
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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