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Entropy in dynamical systems

  1. Title statementEntropy in dynamical systems / Tomasz Downarowicz
    Personal name Downarowicz, Tomasz, 1956- (author)
    Edition statementFirst published
    PublicationNew York : Cambridge University Press, 2011
    Phys.des.xii, 391 stran : schémata
    ISBN978-0-521-88885-1 (vázáno)
    EditionNew mathematical monographs ; 18
    Internal Bibliographies/Indexes NoteObsahuje bibliografii a rejstříky
    Content noteIntroduction; 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
    Subj. Headings entropie entropy * topologie topology * dynamické systémy dynamical systems * teorie řízení control theory * diferenciální rovnice differential equations * integrální rovnice integral equations * dynamické systémy dynamical systems
    Form, Genre učebnice vysokých škol textbooks (higher)
    Conspect519.1/.8 - Kombinatorika. Teorie grafů. Matematická statistika. Operační výzkum. Matematické modelování
    37.016 - Učební osnovy. Vyučovací předměty. Učebnice
    UDC 536.75 , 515.1 , 517.938 , 531.3 , 519.876 , 519.71 , 517.9 , 517.968 , (075.8)
    CountrySpojené státy americké
    Languageangličtina
    Document kindBooks
    URLhttp://assets.cambridge.org/97805218/88851/cover/9780521888851.jpg
    View book information on page www.obalkyknih.cz

    book

    Call numberBarcodeLocationSublocationInfo
    M1/3787 (PřF)3134048444PřFPřF, KMA – RNDr. HronIn-Library Use Only
    Entropy in dynamical systems
    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 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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