Dynamical systems and ergodic theory /:
Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1998.
|
| Schriftenreihe: | London Mathematical Society student texts ;
40. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory. |
| Beschreibung: | 1 online resource (xiii, 179 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781107088955 110708895X 9781139173049 1139173049 |
Internformat
MARC
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| 504 | |a Includes bibliographical references and index. | ||
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| 505 | 0 | |a Cover; Series Page; Title; Copyright; CONTENTS; INTRODUCTION; PRELIMINARIES; 1 Conventions; 2 Notation; 3 Prerequisites in point set topology (CHAPTERs 1-6); 4 Pre-requisites in measure theory (CHAPTERs 7-12); 5 Subadditive sequences; References; CHAPTER 1 EXAMPLES AND BASIC PROPERTIES; 1.1 Examples; 1.2 Transitivity; 1.3 Other characterizations of transitivity; 1.4 Transitivity for subshifts of finite type; 1.5 Minimality and the Birkhoff recurrence theorem; 1.6 Commuting homeomorphisms; 1.7 Comments and references; References | |
| 505 | 8 | |a CHAPTER 2 AN APPLICATION OF RECURRENCE TO ARITHMETIC PROGRESSIONS2.1 Van der Waerden's theorem; 2.2 A dynamical proof; 2.3. The proofs of Sublemma 2.2.2 and Sublemma 2.2.3; 2.4 Comments and references; References; CHAPTER 3 TOPOLOGICAL ENTROPY; 3.1 Definitions; 3.2 The Perron-Frobenious theorem and subshifts of finite type; 3.3 Other definitions and examples; 3.4 Conjugacy; 3.5 Comments and references; References; CHAPTER 4 INTERVAL MAPS; 4.1 Fixed points and periodic points; 4.2 Topological entropy of interval maps; 4.3 Markov maps; 4.4 Comments and references; References | |
| 505 | 8 | |a CHAPTER 5 HYPERBOLIC TORAL AUTOMORPHISMS5.1 Definitions; 5.2 Entropy for Hyperbolic Toral Automorphisms; 5.3 Shadowing and semi-conjugacy; 5.4 Comments and references; References; CHAPTER 6 ROTATION NUMBERS; 6.1 Homeomorphisms of the circle and rotation numbers; 6.2 Denjoy's theorem; 6.3 Comments and references; References; CHAPTER 7 INVARIANT MEASURES; 7.1 Definitions and characterization of invariant measures; 7.2 Borel sigma-algebras for compact metric spaces; 7.3 Examples of invariant measures; 7.4 Invariant measures for other actions; 7.5 Comments and references; References | |
| 505 | 8 | |a CHAPTER 8 MEASURE THEORETIC ENTROPY8.1 Partitions and conditional expectations; 8.2 The entropy of a partition; 8.3 The entropy of a transformation; 8.4 The increasing martingale theorem; 8.5 Entropy and sigma-algebras; 8.6 Conditional entropy; 8.7 Proofs of Lemma 8.7 and Lemma 8.8; 8.8 Isomorphism; 8.9 Comments and references; References; CHAPTER 9 ERGODIC MEASURES; 9.1 Definitions and characterization of ergodic measures; 9.2 Poincare recurrence and Kac's theorem; 9.3 Existence of ergodic measures; 9.4 Some basic constructions in ergodic theory; 9.4.1 Skew products | |
| 505 | 8 | |a 9.4.2 Induced transformations and Rohlin towers9.4.3 Natural extensions; 9.5 Comments and references; References; CHAPTER 10 ERGODIC THEOREMS; 10.1 The Von Neumann ergodic theorem; 10.2 The Birkhoff theorem (for ergodic measures); 10.3 Applications of the ergodic theorems; 10.4 The Birkhoff theorem (for invariant measures); 10.5 Comments and references; References; CHAPTER 11 MIXING PROPERTIES; 11.1 Weak mixing; 11.2 A density one convergence characterization of weak mixing; 11.3 A generalization of the von Neumann ergodic theorem; 11.4 The spectral viewpoint | |
| 520 | |a Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory. | ||
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| 650 | 0 | |a Ergodic theory. |0 http://id.loc.gov/authorities/subjects/sh85044600 | |
| 650 | 6 | |a Dynamique topologique. | |
| 650 | 6 | |a Théorie ergodique. | |
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| contents | Cover; Series Page; Title; Copyright; CONTENTS; INTRODUCTION; PRELIMINARIES; 1 Conventions; 2 Notation; 3 Prerequisites in point set topology (CHAPTERs 1-6); 4 Pre-requisites in measure theory (CHAPTERs 7-12); 5 Subadditive sequences; References; CHAPTER 1 EXAMPLES AND BASIC PROPERTIES; 1.1 Examples; 1.2 Transitivity; 1.3 Other characterizations of transitivity; 1.4 Transitivity for subshifts of finite type; 1.5 Minimality and the Birkhoff recurrence theorem; 1.6 Commuting homeomorphisms; 1.7 Comments and references; References CHAPTER 2 AN APPLICATION OF RECURRENCE TO ARITHMETIC PROGRESSIONS2.1 Van der Waerden's theorem; 2.2 A dynamical proof; 2.3. The proofs of Sublemma 2.2.2 and Sublemma 2.2.3; 2.4 Comments and references; References; CHAPTER 3 TOPOLOGICAL ENTROPY; 3.1 Definitions; 3.2 The Perron-Frobenious theorem and subshifts of finite type; 3.3 Other definitions and examples; 3.4 Conjugacy; 3.5 Comments and references; References; CHAPTER 4 INTERVAL MAPS; 4.1 Fixed points and periodic points; 4.2 Topological entropy of interval maps; 4.3 Markov maps; 4.4 Comments and references; References CHAPTER 5 HYPERBOLIC TORAL AUTOMORPHISMS5.1 Definitions; 5.2 Entropy for Hyperbolic Toral Automorphisms; 5.3 Shadowing and semi-conjugacy; 5.4 Comments and references; References; CHAPTER 6 ROTATION NUMBERS; 6.1 Homeomorphisms of the circle and rotation numbers; 6.2 Denjoy's theorem; 6.3 Comments and references; References; CHAPTER 7 INVARIANT MEASURES; 7.1 Definitions and characterization of invariant measures; 7.2 Borel sigma-algebras for compact metric spaces; 7.3 Examples of invariant measures; 7.4 Invariant measures for other actions; 7.5 Comments and references; References CHAPTER 8 MEASURE THEORETIC ENTROPY8.1 Partitions and conditional expectations; 8.2 The entropy of a partition; 8.3 The entropy of a transformation; 8.4 The increasing martingale theorem; 8.5 Entropy and sigma-algebras; 8.6 Conditional entropy; 8.7 Proofs of Lemma 8.7 and Lemma 8.8; 8.8 Isomorphism; 8.9 Comments and references; References; CHAPTER 9 ERGODIC MEASURES; 9.1 Definitions and characterization of ergodic measures; 9.2 Poincare recurrence and Kac's theorem; 9.3 Existence of ergodic measures; 9.4 Some basic constructions in ergodic theory; 9.4.1 Skew products 9.4.2 Induced transformations and Rohlin towers9.4.3 Natural extensions; 9.5 Comments and references; References; CHAPTER 10 ERGODIC THEOREMS; 10.1 The Von Neumann ergodic theorem; 10.2 The Birkhoff theorem (for ergodic measures); 10.3 Applications of the ergodic theorems; 10.4 The Birkhoff theorem (for invariant measures); 10.5 Comments and references; References; CHAPTER 11 MIXING PROPERTIES; 11.1 Weak mixing; 11.2 A density one convergence characterization of weak mixing; 11.3 A generalization of the von Neumann ergodic theorem; 11.4 The spectral viewpoint |
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| id | ZDB-4-EBA-ocn852896242 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:26Z |
| institution | BVB |
| isbn | 9781107088955 110708895X 9781139173049 1139173049 |
| language | English |
| oclc_num | 852896242 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 179 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society student texts ; |
| series2 | London Mathematical Society student texts ; |
| spelling | Pollicott, Mark. Dynamical systems and ergodic theory / Mark Pollicott, Michiko Yuri. Cambridge ; New York : Cambridge University Press, 1998. 1 online resource (xiii, 179 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society student texts ; 40 Includes bibliographical references and index. Print version record. Cover; Series Page; Title; Copyright; CONTENTS; INTRODUCTION; PRELIMINARIES; 1 Conventions; 2 Notation; 3 Prerequisites in point set topology (CHAPTERs 1-6); 4 Pre-requisites in measure theory (CHAPTERs 7-12); 5 Subadditive sequences; References; CHAPTER 1 EXAMPLES AND BASIC PROPERTIES; 1.1 Examples; 1.2 Transitivity; 1.3 Other characterizations of transitivity; 1.4 Transitivity for subshifts of finite type; 1.5 Minimality and the Birkhoff recurrence theorem; 1.6 Commuting homeomorphisms; 1.7 Comments and references; References CHAPTER 2 AN APPLICATION OF RECURRENCE TO ARITHMETIC PROGRESSIONS2.1 Van der Waerden's theorem; 2.2 A dynamical proof; 2.3. The proofs of Sublemma 2.2.2 and Sublemma 2.2.3; 2.4 Comments and references; References; CHAPTER 3 TOPOLOGICAL ENTROPY; 3.1 Definitions; 3.2 The Perron-Frobenious theorem and subshifts of finite type; 3.3 Other definitions and examples; 3.4 Conjugacy; 3.5 Comments and references; References; CHAPTER 4 INTERVAL MAPS; 4.1 Fixed points and periodic points; 4.2 Topological entropy of interval maps; 4.3 Markov maps; 4.4 Comments and references; References CHAPTER 5 HYPERBOLIC TORAL AUTOMORPHISMS5.1 Definitions; 5.2 Entropy for Hyperbolic Toral Automorphisms; 5.3 Shadowing and semi-conjugacy; 5.4 Comments and references; References; CHAPTER 6 ROTATION NUMBERS; 6.1 Homeomorphisms of the circle and rotation numbers; 6.2 Denjoy's theorem; 6.3 Comments and references; References; CHAPTER 7 INVARIANT MEASURES; 7.1 Definitions and characterization of invariant measures; 7.2 Borel sigma-algebras for compact metric spaces; 7.3 Examples of invariant measures; 7.4 Invariant measures for other actions; 7.5 Comments and references; References CHAPTER 8 MEASURE THEORETIC ENTROPY8.1 Partitions and conditional expectations; 8.2 The entropy of a partition; 8.3 The entropy of a transformation; 8.4 The increasing martingale theorem; 8.5 Entropy and sigma-algebras; 8.6 Conditional entropy; 8.7 Proofs of Lemma 8.7 and Lemma 8.8; 8.8 Isomorphism; 8.9 Comments and references; References; CHAPTER 9 ERGODIC MEASURES; 9.1 Definitions and characterization of ergodic measures; 9.2 Poincare recurrence and Kac's theorem; 9.3 Existence of ergodic measures; 9.4 Some basic constructions in ergodic theory; 9.4.1 Skew products 9.4.2 Induced transformations and Rohlin towers9.4.3 Natural extensions; 9.5 Comments and references; References; CHAPTER 10 ERGODIC THEOREMS; 10.1 The Von Neumann ergodic theorem; 10.2 The Birkhoff theorem (for ergodic measures); 10.3 Applications of the ergodic theorems; 10.4 The Birkhoff theorem (for invariant measures); 10.5 Comments and references; References; CHAPTER 11 MIXING PROPERTIES; 11.1 Weak mixing; 11.2 A density one convergence characterization of weak mixing; 11.3 A generalization of the von Neumann ergodic theorem; 11.4 The spectral viewpoint Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory. Topological dynamics. http://id.loc.gov/authorities/subjects/sh85136080 Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Dynamique topologique. Théorie ergodique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Ergodic theory fast Topological dynamics fast Dynamisches System gnd Ergodentheorie gnd http://d-nb.info/gnd/4015246-7 Ergodiciteit. gtt Dynamische systemen. gtt Dynamique topologique. ram Théorie ergodique. ram Yuri, Michiko, 1956- https://id.oclc.org/worldcat/entity/E39PCjGVC3wPJ7hHBphBrvGx9P http://id.loc.gov/authorities/names/n97053106 Print version: Pollicott, Mark. Dynamical systems and ergodic theory. Cambridge ; New York : Cambridge University Press, 1998 0521572940 (DLC) 97008812 (OCoLC)37106946 London Mathematical Society student texts ; 40. http://id.loc.gov/authorities/names/n84727069 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=570398 Volltext |
| spellingShingle | Pollicott, Mark Dynamical systems and ergodic theory / London Mathematical Society student texts ; Cover; Series Page; Title; Copyright; CONTENTS; INTRODUCTION; PRELIMINARIES; 1 Conventions; 2 Notation; 3 Prerequisites in point set topology (CHAPTERs 1-6); 4 Pre-requisites in measure theory (CHAPTERs 7-12); 5 Subadditive sequences; References; CHAPTER 1 EXAMPLES AND BASIC PROPERTIES; 1.1 Examples; 1.2 Transitivity; 1.3 Other characterizations of transitivity; 1.4 Transitivity for subshifts of finite type; 1.5 Minimality and the Birkhoff recurrence theorem; 1.6 Commuting homeomorphisms; 1.7 Comments and references; References CHAPTER 2 AN APPLICATION OF RECURRENCE TO ARITHMETIC PROGRESSIONS2.1 Van der Waerden's theorem; 2.2 A dynamical proof; 2.3. The proofs of Sublemma 2.2.2 and Sublemma 2.2.3; 2.4 Comments and references; References; CHAPTER 3 TOPOLOGICAL ENTROPY; 3.1 Definitions; 3.2 The Perron-Frobenious theorem and subshifts of finite type; 3.3 Other definitions and examples; 3.4 Conjugacy; 3.5 Comments and references; References; CHAPTER 4 INTERVAL MAPS; 4.1 Fixed points and periodic points; 4.2 Topological entropy of interval maps; 4.3 Markov maps; 4.4 Comments and references; References CHAPTER 5 HYPERBOLIC TORAL AUTOMORPHISMS5.1 Definitions; 5.2 Entropy for Hyperbolic Toral Automorphisms; 5.3 Shadowing and semi-conjugacy; 5.4 Comments and references; References; CHAPTER 6 ROTATION NUMBERS; 6.1 Homeomorphisms of the circle and rotation numbers; 6.2 Denjoy's theorem; 6.3 Comments and references; References; CHAPTER 7 INVARIANT MEASURES; 7.1 Definitions and characterization of invariant measures; 7.2 Borel sigma-algebras for compact metric spaces; 7.3 Examples of invariant measures; 7.4 Invariant measures for other actions; 7.5 Comments and references; References CHAPTER 8 MEASURE THEORETIC ENTROPY8.1 Partitions and conditional expectations; 8.2 The entropy of a partition; 8.3 The entropy of a transformation; 8.4 The increasing martingale theorem; 8.5 Entropy and sigma-algebras; 8.6 Conditional entropy; 8.7 Proofs of Lemma 8.7 and Lemma 8.8; 8.8 Isomorphism; 8.9 Comments and references; References; CHAPTER 9 ERGODIC MEASURES; 9.1 Definitions and characterization of ergodic measures; 9.2 Poincare recurrence and Kac's theorem; 9.3 Existence of ergodic measures; 9.4 Some basic constructions in ergodic theory; 9.4.1 Skew products 9.4.2 Induced transformations and Rohlin towers9.4.3 Natural extensions; 9.5 Comments and references; References; CHAPTER 10 ERGODIC THEOREMS; 10.1 The Von Neumann ergodic theorem; 10.2 The Birkhoff theorem (for ergodic measures); 10.3 Applications of the ergodic theorems; 10.4 The Birkhoff theorem (for invariant measures); 10.5 Comments and references; References; CHAPTER 11 MIXING PROPERTIES; 11.1 Weak mixing; 11.2 A density one convergence characterization of weak mixing; 11.3 A generalization of the von Neumann ergodic theorem; 11.4 The spectral viewpoint Topological dynamics. http://id.loc.gov/authorities/subjects/sh85136080 Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Dynamique topologique. Théorie ergodique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Ergodic theory fast Topological dynamics fast Dynamisches System gnd Ergodentheorie gnd http://d-nb.info/gnd/4015246-7 Ergodiciteit. gtt Dynamische systemen. gtt Dynamique topologique. ram Théorie ergodique. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85136080 http://id.loc.gov/authorities/subjects/sh85044600 http://d-nb.info/gnd/4015246-7 |
| title | Dynamical systems and ergodic theory / |
| title_auth | Dynamical systems and ergodic theory / |
| title_exact_search | Dynamical systems and ergodic theory / |
| title_full | Dynamical systems and ergodic theory / Mark Pollicott, Michiko Yuri. |
| title_fullStr | Dynamical systems and ergodic theory / Mark Pollicott, Michiko Yuri. |
| title_full_unstemmed | Dynamical systems and ergodic theory / Mark Pollicott, Michiko Yuri. |
| title_short | Dynamical systems and ergodic theory / |
| title_sort | dynamical systems and ergodic theory |
| topic | Topological dynamics. http://id.loc.gov/authorities/subjects/sh85136080 Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Dynamique topologique. Théorie ergodique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Ergodic theory fast Topological dynamics fast Dynamisches System gnd Ergodentheorie gnd http://d-nb.info/gnd/4015246-7 Ergodiciteit. gtt Dynamische systemen. gtt Dynamique topologique. ram Théorie ergodique. ram |
| topic_facet | Topological dynamics. Ergodic theory. Dynamique topologique. Théorie ergodique. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Ergodic theory Topological dynamics Dynamisches System Ergodentheorie Ergodiciteit. Dynamische systemen. |
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| work_keys_str_mv | AT pollicottmark dynamicalsystemsandergodictheory AT yurimichiko dynamicalsystemsandergodictheory |