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EBOOK
Author Kerr, David,
Title Ergodic theory : independence and dichotomies / David Kerr, Hanfeng Li.
Imprint Cham, Switzerland : Springer, 2016.

LOCATION CALL # STATUS MESSAGE
 OHIOLINK SPRINGER EBOOKS    ONLINE  
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Author Kerr, David,
Series Springer monographs in mathematics
Springer monographs in mathematics.
Subject Ergodic theory.
Alt Name Li, Hanfeng,
LOCATION CALL # STATUS MESSAGE
 OHIOLINK SPRINGER EBOOKS    ONLINE  
View online
Author Kerr, David,
Series Springer monographs in mathematics
Springer monographs in mathematics.
Subject Ergodic theory.
Alt Name Li, Hanfeng,
Description 1 online resource.
polychrome rdacc
Contents 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.
Summary 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.
Bibliography Note Includes bibliographical references.
Note Online resource; title from PDF title page (SpringerLink, viewed February 16, 2017).
ISBN 9783319498478 (electronic bk.)
3319498479 (electronic bk.)
3319498452
9783319498454
9783319498454 (print)
ISBN/ISSN 10.1007/978-3-319-49847-8
OCLC # 972331008
Additional Format Printed edition: 9783319498454


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