Entropy in dynamical systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2011
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | New Mathematical Monographs
18 |
| Schlagworte: | |
| Online-Zugang: | Cover image Inhaltsverzeichnis |
| Beschreibung: | "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. Includes bibliographical references (pages [379]-385) and index |
| Beschreibung: | XII, 391 S. 24 cm |
| ISBN: | 9780521888851 |
Internformat
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| 500 | |a Includes bibliographical references (pages [379]-385) and index | ||
| 650 | 4 | |a Topological entropy |v Textbooks | |
| 650 | 4 | |a Topological dynamics |v Textbooks | |
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Datensatz im Suchindex
| _version_ | 1804148608824508416 |
|---|---|
| adam_text | ENTROPY IN DYNAMICAL SYSTEMS
/ DOWNAROWICZ, TOMASZ
: 2011, 2011
TABLE OF CONTENTS / INHALTSVERZEICHNIS
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.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| author | Downarowicz, Tomasz 1956- |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 810 |
| ctrlnum | (OCoLC)694616470 (DE-599)BVBBV039727571 |
| dewey-full | 515/.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.39 |
| dewey-search | 515/.39 |
| dewey-sort | 3515 239 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| institution | BVB |
| isbn | 9780521888851 |
| language | English |
| lccn | 2010050336 |
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| physical | XII, 391 S. 24 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge University Press |
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| series | New Mathematical Monographs |
| series2 | New Mathematical Monographs |
| spelling | Downarowicz, Tomasz 1956- Verfasser (DE-588)1022446428 aut Entropy in dynamical systems Tomasz Downarowicz 1. publ. Cambridge Cambridge University Press 2011 XII, 391 S. 24 cm txt rdacontent n rdamedia nc rdacarrier New Mathematical Monographs 18 "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. Includes bibliographical references (pages [379]-385) and index Topological entropy Textbooks Topological dynamics Textbooks MATHEMATICS / General bisacsh Dynamisches System (DE-588)4013396-5 gnd rswk-swf Topologische Entropie (DE-588)4528188-9 gnd rswk-swf Topologische Entropie (DE-588)4528188-9 s Dynamisches System (DE-588)4013396-5 s DE-604 New Mathematical Monographs 18 (DE-604)BV035420183 18 http://assets.cambridge.org/97805218/88851/cover/9780521888851.jpg Cover image LoC Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024575546&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Downarowicz, Tomasz 1956- Entropy in dynamical systems New Mathematical Monographs Topological entropy Textbooks Topological dynamics Textbooks MATHEMATICS / General bisacsh Dynamisches System (DE-588)4013396-5 gnd Topologische Entropie (DE-588)4528188-9 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4528188-9 |
| title | Entropy in dynamical systems |
| title_auth | Entropy in dynamical systems |
| title_exact_search | Entropy in dynamical systems |
| title_full | Entropy in dynamical systems Tomasz Downarowicz |
| title_fullStr | Entropy in dynamical systems Tomasz Downarowicz |
| title_full_unstemmed | Entropy in dynamical systems Tomasz Downarowicz |
| title_short | Entropy in dynamical systems |
| title_sort | entropy in dynamical systems |
| topic | Topological entropy Textbooks Topological dynamics Textbooks MATHEMATICS / General bisacsh Dynamisches System (DE-588)4013396-5 gnd Topologische Entropie (DE-588)4528188-9 gnd |
| topic_facet | Topological entropy Textbooks Topological dynamics Textbooks MATHEMATICS / General Dynamisches System Topologische Entropie |
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