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Cover: 9783319842547 | Ergodic Theory | Independence and Dichotomies | Hanfeng Li (u. a.)
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Ergodic Theory
Independence and Dichotomies
Taschenbuch von Hanfeng Li (u. a.)
Sprache: Englisch

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Beschreibung
This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing, compactness, entropy, and amenability. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy.

The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.
This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing, compactness, entropy, and amenability. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy.

The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.
Zusammenfassung

Provides an introduction to the ergodic theory and topological dynamics of actions of general countable groups

Covers several topics of current research interest, including Popa's cocycle superrigidity, sofic entropy, and algebraic actions

Contains a consolidated account of amenability and its ramifications for dynamics, including a systematic exposition of the entropy theory for actions of amenable groups

Includes supplementary material: [...]

Inhaltsverzeichnis
Preface.- Introduction.- General Framework and Notational Conventions.- Part 1 Weak Mixing Comactness.- Basic Concepts in Ergodic Theory.- Structure Theory for P.M.P. Actions.- Amenability.- Property (T).- Orbit Equivalence Beyond Amenability.- Topological Dynamics.- Tameness and Independence.- Part 2 Entropy.- Entropy for Actions of Amenable Groups.- Entropy for Actions of Sofic Groups.- The f-invariant.- Entropy and Independence.- Algebraic Actions: Expansiveness, Homoclinicity, and Entropy.- Algebraic Actions: Entropy and the Fuglede-Kadison Determinant.- Appendix A. Polish Spaces and Standard Borel Spaces.- Appendix B. Positive Definite Functions and Weak Containment.- Appendix C. Hilbert Modules.- Appendix D. Weakly Almost Periodic Functions.- Appendix E. Gaussian Actions.
Details
Erscheinungsjahr: 2018
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Springer Monographs in Mathematics
Inhalt: xxxiv
431 S.
ISBN-13: 9783319842547
ISBN-10: 3319842544
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Li, Hanfeng
Kerr, David
Auflage: Softcover reprint of the original 1st ed. 2016
Hersteller: Springer International Publishing
Springer International Publishing AG
Springer Monographs in Mathematics
Maße: 235 x 155 x 26 mm
Von/Mit: Hanfeng Li (u. a.)
Erscheinungsdatum: 13.07.2018
Gewicht: 0,703 kg
Artikel-ID: 114238382
Zusammenfassung

Provides an introduction to the ergodic theory and topological dynamics of actions of general countable groups

Covers several topics of current research interest, including Popa's cocycle superrigidity, sofic entropy, and algebraic actions

Contains a consolidated account of amenability and its ramifications for dynamics, including a systematic exposition of the entropy theory for actions of amenable groups

Includes supplementary material: [...]

Inhaltsverzeichnis
Preface.- Introduction.- General Framework and Notational Conventions.- Part 1 Weak Mixing Comactness.- Basic Concepts in Ergodic Theory.- Structure Theory for P.M.P. Actions.- Amenability.- Property (T).- Orbit Equivalence Beyond Amenability.- Topological Dynamics.- Tameness and Independence.- Part 2 Entropy.- Entropy for Actions of Amenable Groups.- Entropy for Actions of Sofic Groups.- The f-invariant.- Entropy and Independence.- Algebraic Actions: Expansiveness, Homoclinicity, and Entropy.- Algebraic Actions: Entropy and the Fuglede-Kadison Determinant.- Appendix A. Polish Spaces and Standard Borel Spaces.- Appendix B. Positive Definite Functions and Weak Containment.- Appendix C. Hilbert Modules.- Appendix D. Weakly Almost Periodic Functions.- Appendix E. Gaussian Actions.
Details
Erscheinungsjahr: 2018
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Springer Monographs in Mathematics
Inhalt: xxxiv
431 S.
ISBN-13: 9783319842547
ISBN-10: 3319842544
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Li, Hanfeng
Kerr, David
Auflage: Softcover reprint of the original 1st ed. 2016
Hersteller: Springer International Publishing
Springer International Publishing AG
Springer Monographs in Mathematics
Maße: 235 x 155 x 26 mm
Von/Mit: Hanfeng Li (u. a.)
Erscheinungsdatum: 13.07.2018
Gewicht: 0,703 kg
Artikel-ID: 114238382
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