Classification problems in ergodic theory /:
The isomorphism problem of ergodic theory has been extensively studied since Kolmogorov's introduction of entropy into the subject and especially since Ornstein's solution for Bernoulli processes. Much of this research has been in the abstract measure-theoretic setting of pure ergodic theo...
Gespeichert in:
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
1982.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
67. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The isomorphism problem of ergodic theory has been extensively studied since Kolmogorov's introduction of entropy into the subject and especially since Ornstein's solution for Bernoulli processes. Much of this research has been in the abstract measure-theoretic setting of pure ergodic theory. However, there has been growing interest in isomorphisms of a more restrictive and perhaps more realistic nature which recognize and respect the state structure of processes in various ways. These notes give an account of some recent developments in this direction. A special feature is the frequent use of the information function as an invariant in a variety of special isomorphism problems. Lecturers and postgraduates in mathematics and research workers in communication engineering will find this book of use and interest. |
| Beschreibung: | 1 online resource (101 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 96-99) and index. |
| ISBN: | 9781107361201 1107361206 9780511892165 0511892160 |
| ISSN: | 0076-0552 ; |
Internformat
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| 245 | 1 | 0 | |a Classification problems in ergodic theory / |c William Parry and Selim Tuncel. |
| 260 | |a Cambridge [Cambridgeshire] ; |a New York : |b Cambridge University Press, |c 1982. | ||
| 300 | |a 1 online resource (101 pages) : |b illustrations | ||
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| 490 | 1 | |a London Mathematical Society lecture note series, |x 0076-0552 ; |v 67 | |
| 504 | |a Includes bibliographical references (pages 96-99) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a The isomorphism problem of ergodic theory has been extensively studied since Kolmogorov's introduction of entropy into the subject and especially since Ornstein's solution for Bernoulli processes. Much of this research has been in the abstract measure-theoretic setting of pure ergodic theory. However, there has been growing interest in isomorphisms of a more restrictive and perhaps more realistic nature which recognize and respect the state structure of processes in various ways. These notes give an account of some recent developments in this direction. A special feature is the frequent use of the information function as an invariant in a variety of special isomorphism problems. Lecturers and postgraduates in mathematics and research workers in communication engineering will find this book of use and interest. | ||
| 505 | 0 | |a Cover; Title; Copyright; Contents; Preface; Chapter I: Introduction; 1. Motivation; 2. Basic Definitions and Conventions; 3. Processes; 4. Markov Chains; 5. Reduced Processes and Topological Markov Chains; 6. Information and Entropy; 7. Types of Classification; Chapter II: The Information Cocycle; 1. Regular Isomorphisms; 2. Unitary Operators and Cocycles; 3. Information Variance; 4. The Variational Principle for Topological Markov Chains; 5. A Group Invariant; 6. Quasi-regular Isomorphisms and Bounded Codes; 7. Central Limiting Distributions as Invariants; Chapter III: Finitary Isomorphisms | |
| 505 | 8 | |a 1. The Marker Method2. Finite Expected Code-lengths; Chapter IV: Block-codes; 1. Continuity and Block-codes; 2. Bounded-to-one Codes; 3. Suspensions and Winding Numbers; 4. Computation of the First Cohomology Group; Chapter V: Classifications of Topological Markov Chains; 1. Finite Equivalence; 2. Almost Topological Conjugacy and the Road Problem; 3. Topological Conjugacy of Topological Markov Chains; 4. Invariants and Reversibility; 5. Flow Equivalence; Appendix: Shannon's Work on Maximal Measures; References; Index | |
| 650 | 0 | |a Ergodic theory. |0 http://id.loc.gov/authorities/subjects/sh85044600 | |
| 650 | 0 | |a Isomorphisms (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85068654 | |
| 650 | 6 | |a Théorie ergodique. | |
| 650 | 6 | |a Isomorphismes (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Ergodic theory |2 fast | |
| 650 | 7 | |a Isomorphisms (Mathematics) |2 fast | |
| 650 | 7 | |a Ergodentheorie |2 gnd |0 http://d-nb.info/gnd/4015246-7 | |
| 650 | 7 | |a Théorie ergodique. |2 ram | |
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| 700 | 1 | |a Tuncel, Selim. | |
| 758 | |i has work: |a Classification problems in ergodic theory (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFFQjHxJpv7CYvpBFJRV83 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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Datensatz im Suchindex
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| _version_ | 1816882229025964032 |
| adam_text | |
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| author | Parry, William, 1934-2006 |
| author2 | Tuncel, Selim |
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| author2_variant | s t st |
| author_GND | http://id.loc.gov/authorities/names/n79075589 |
| author_facet | Parry, William, 1934-2006 Tuncel, Selim |
| author_role | |
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| contents | Cover; Title; Copyright; Contents; Preface; Chapter I: Introduction; 1. Motivation; 2. Basic Definitions and Conventions; 3. Processes; 4. Markov Chains; 5. Reduced Processes and Topological Markov Chains; 6. Information and Entropy; 7. Types of Classification; Chapter II: The Information Cocycle; 1. Regular Isomorphisms; 2. Unitary Operators and Cocycles; 3. Information Variance; 4. The Variational Principle for Topological Markov Chains; 5. A Group Invariant; 6. Quasi-regular Isomorphisms and Bounded Codes; 7. Central Limiting Distributions as Invariants; Chapter III: Finitary Isomorphisms 1. The Marker Method2. Finite Expected Code-lengths; Chapter IV: Block-codes; 1. Continuity and Block-codes; 2. Bounded-to-one Codes; 3. Suspensions and Winding Numbers; 4. Computation of the First Cohomology Group; Chapter V: Classifications of Topological Markov Chains; 1. Finite Equivalence; 2. Almost Topological Conjugacy and the Road Problem; 3. Topological Conjugacy of Topological Markov Chains; 4. Invariants and Reversibility; 5. Flow Equivalence; Appendix: Shannon's Work on Maximal Measures; References; Index |
| ctrlnum | (OCoLC)839304303 |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:17Z |
| institution | BVB |
| isbn | 9781107361201 1107361206 9780511892165 0511892160 |
| issn | 0076-0552 ; |
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| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series, |
| spelling | Parry, William, 1934-2006. https://id.oclc.org/worldcat/entity/E39PBJgRRWkpdjC9H7BbQ9WMT3 http://id.loc.gov/authorities/names/n79075589 Classification problems in ergodic theory / William Parry and Selim Tuncel. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1982. 1 online resource (101 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series, 0076-0552 ; 67 Includes bibliographical references (pages 96-99) and index. Print version record. The isomorphism problem of ergodic theory has been extensively studied since Kolmogorov's introduction of entropy into the subject and especially since Ornstein's solution for Bernoulli processes. Much of this research has been in the abstract measure-theoretic setting of pure ergodic theory. However, there has been growing interest in isomorphisms of a more restrictive and perhaps more realistic nature which recognize and respect the state structure of processes in various ways. These notes give an account of some recent developments in this direction. A special feature is the frequent use of the information function as an invariant in a variety of special isomorphism problems. Lecturers and postgraduates in mathematics and research workers in communication engineering will find this book of use and interest. Cover; Title; Copyright; Contents; Preface; Chapter I: Introduction; 1. Motivation; 2. Basic Definitions and Conventions; 3. Processes; 4. Markov Chains; 5. Reduced Processes and Topological Markov Chains; 6. Information and Entropy; 7. Types of Classification; Chapter II: The Information Cocycle; 1. Regular Isomorphisms; 2. Unitary Operators and Cocycles; 3. Information Variance; 4. The Variational Principle for Topological Markov Chains; 5. A Group Invariant; 6. Quasi-regular Isomorphisms and Bounded Codes; 7. Central Limiting Distributions as Invariants; Chapter III: Finitary Isomorphisms 1. The Marker Method2. Finite Expected Code-lengths; Chapter IV: Block-codes; 1. Continuity and Block-codes; 2. Bounded-to-one Codes; 3. Suspensions and Winding Numbers; 4. Computation of the First Cohomology Group; Chapter V: Classifications of Topological Markov Chains; 1. Finite Equivalence; 2. Almost Topological Conjugacy and the Road Problem; 3. Topological Conjugacy of Topological Markov Chains; 4. Invariants and Reversibility; 5. Flow Equivalence; Appendix: Shannon's Work on Maximal Measures; References; Index Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Isomorphisms (Mathematics) http://id.loc.gov/authorities/subjects/sh85068654 Théorie ergodique. Isomorphismes (Mathématiques) MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Ergodic theory fast Isomorphisms (Mathematics) fast Ergodentheorie gnd http://d-nb.info/gnd/4015246-7 Théorie ergodique. ram Isomorphismes (mathématiques) ram Tuncel, Selim. has work: Classification problems in ergodic theory (Text) https://id.oclc.org/worldcat/entity/E39PCFFQjHxJpv7CYvpBFJRV83 https://id.oclc.org/worldcat/ontology/hasWork Print version: Parry, William, 1934-2006. Classification problems in ergodic theory. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1982 0521287944 (DLC) 82004350 (OCoLC)8388077 London Mathematical Society lecture note series ; 67. 0076-0552 http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552523 Volltext |
| spellingShingle | Parry, William, 1934-2006 Classification problems in ergodic theory / London Mathematical Society lecture note series ; Cover; Title; Copyright; Contents; Preface; Chapter I: Introduction; 1. Motivation; 2. Basic Definitions and Conventions; 3. Processes; 4. Markov Chains; 5. Reduced Processes and Topological Markov Chains; 6. Information and Entropy; 7. Types of Classification; Chapter II: The Information Cocycle; 1. Regular Isomorphisms; 2. Unitary Operators and Cocycles; 3. Information Variance; 4. The Variational Principle for Topological Markov Chains; 5. A Group Invariant; 6. Quasi-regular Isomorphisms and Bounded Codes; 7. Central Limiting Distributions as Invariants; Chapter III: Finitary Isomorphisms 1. The Marker Method2. Finite Expected Code-lengths; Chapter IV: Block-codes; 1. Continuity and Block-codes; 2. Bounded-to-one Codes; 3. Suspensions and Winding Numbers; 4. Computation of the First Cohomology Group; Chapter V: Classifications of Topological Markov Chains; 1. Finite Equivalence; 2. Almost Topological Conjugacy and the Road Problem; 3. Topological Conjugacy of Topological Markov Chains; 4. Invariants and Reversibility; 5. Flow Equivalence; Appendix: Shannon's Work on Maximal Measures; References; Index Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Isomorphisms (Mathematics) http://id.loc.gov/authorities/subjects/sh85068654 Théorie ergodique. Isomorphismes (Mathématiques) MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Ergodic theory fast Isomorphisms (Mathematics) fast Ergodentheorie gnd http://d-nb.info/gnd/4015246-7 Théorie ergodique. ram Isomorphismes (mathématiques) ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85044600 http://id.loc.gov/authorities/subjects/sh85068654 http://d-nb.info/gnd/4015246-7 |
| title | Classification problems in ergodic theory / |
| title_auth | Classification problems in ergodic theory / |
| title_exact_search | Classification problems in ergodic theory / |
| title_full | Classification problems in ergodic theory / William Parry and Selim Tuncel. |
| title_fullStr | Classification problems in ergodic theory / William Parry and Selim Tuncel. |
| title_full_unstemmed | Classification problems in ergodic theory / William Parry and Selim Tuncel. |
| title_short | Classification problems in ergodic theory / |
| title_sort | classification problems in ergodic theory |
| topic | Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Isomorphisms (Mathematics) http://id.loc.gov/authorities/subjects/sh85068654 Théorie ergodique. Isomorphismes (Mathématiques) MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Ergodic theory fast Isomorphisms (Mathematics) fast Ergodentheorie gnd http://d-nb.info/gnd/4015246-7 Théorie ergodique. ram Isomorphismes (mathématiques) ram |
| topic_facet | Ergodic theory. Isomorphisms (Mathematics) Théorie ergodique. Isomorphismes (Mathématiques) MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Ergodic theory Ergodentheorie Isomorphismes (mathématiques) |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552523 |
| work_keys_str_mv | AT parrywilliam classificationproblemsinergodictheory AT tuncelselim classificationproblemsinergodictheory |