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010 a| 2010050336;

020 a| 9780521888851 (hardback);

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050 00 a| QA611.5b| .D685 2011;

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084 a| MAT0000002| bisacsh;

100 1 a| Downarowicz, Tomasz,d| 1956-?| UNAUTHORIZED;

245 10 a| Entropy in Dynamical Systemsh| [electronic resource] /c| Tomasz Downarowicz.;

260 a| Cambridge ;a| New York :b| Cambridge University Press,;

300 a| xii, 391 pages ;c| 24 cm.;

490 0 a| New Mathematical Monographs ;v| 18;

504 a| Includes bibliographical references (pages [379]-385) and index.;

505 8 a| Machine generated contents note: 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.;

506 a| Available only to authorized users.;

520 a| "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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Topological entropyv| Textbooks.=| ^A489319;

650 0 a| Topological dynamicsv| Textbooks.=| ^A18060;

650 7 a| MATHEMATICS / General2| bisacsh.;

655 0 a| Electronic books.=| ^A491897;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=807302;

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Entropy in Dynamical Systems / Tomasz Downarowicz.

Author/creator	Downarowicz, Tomasz, 1956-
Format	Electronic
Publication Info	Cambridge ; New York : Cambridge University Press,
Description	xii, 391 pages ; 24 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Topological entropy--Textbooks. Topological dynamics--Textbooks.

Series	New Mathematical Monographs ; 18
Contents	Machine generated contents note: 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.
Abstract	"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"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages [379]-385) and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2010050336
ISBN	9780521888851 (hardback)

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