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 Genera...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2011
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| Schriftenreihe: | New mathematical monographs
18 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xii, 391 pages) |
| ISBN: | 9780511976155 |
| DOI: | 10.1017/CBO9780511976155 |
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| 245 | 1 | 0 | |a Entropy in Dynamical Systems |c Tomasz Downarowicz |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a 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. | |
| 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 | ||
| 650 | 4 | |a Topological entropy / Textbooks | |
| 650 | 4 | |a Topological dynamics / Textbooks | |
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Datensatz im Suchindex
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| author | Downarowicz, Tomasz 1956- |
| author_facet | Downarowicz, Tomasz 1956- |
| author_role | aut |
| author_sort | Downarowicz, Tomasz 1956- |
| author_variant | t d td |
| building | Verbundindex |
| bvnumber | BV043941695 |
| classification_rvk | SK 810 |
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| contents | 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. |
| ctrlnum | (ZDB-20-CBO)CR9780511976155 (OCoLC)852524157 (DE-599)BVBBV043941695 |
| 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 |
| doi_str_mv | 10.1017/CBO9780511976155 |
| format | Electronic eBook |
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| id | DE-604.BV043941695 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511976155 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350665 |
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| physical | 1 online resource (xii, 391 pages) |
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| publishDate | 2011 |
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| publisher | Cambridge University Press |
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| spelling | Downarowicz, Tomasz 1956- Verfasser aut Entropy in Dynamical Systems Tomasz Downarowicz Cambridge Cambridge University Press 2011 1 online resource (xii, 391 pages) txt rdacontent c rdamedia cr rdacarrier New mathematical monographs 18 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 Topological entropy / Textbooks Topological dynamics / Textbooks 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 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-88885-1 https://doi.org/10.1017/CBO9780511976155 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Downarowicz, Tomasz 1956- Entropy in Dynamical Systems 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. Topological entropy / Textbooks Topological dynamics / Textbooks 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 Dynamisches System (DE-588)4013396-5 gnd Topologische Entropie (DE-588)4528188-9 gnd |
| topic_facet | Topological entropy / Textbooks Topological dynamics / Textbooks Dynamisches System Topologische Entropie |
| url | https://doi.org/10.1017/CBO9780511976155 |
| work_keys_str_mv | AT downarowicztomasz entropyindynamicalsystems |