
Ergodic Theory
Independence and Dichotomies
Springer (Publisher)
Published on 13. July 2018
Book
Paperback/Softback
XXXIV, 431 pages
978-3-319-84254-7 (ISBN)
Description
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.
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.
More details
Product info
Previously published in hardcover
Series
Edition
Softcover reprint of the original 1st ed. 2016
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
XXXIV, 431 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 26 mm
Weight
703 gr
ISBN-13
978-3-319-84254-7 (9783319842547)
DOI
10.1007/978-3-319-49847-8
Schweitzer Classification
Other editions
Additional editions

Book
02/2017
1st Edition
Springer
€160.49
Shipment within 10-15 days
Persons
Thierry Giordano is a Professor at the University of Ottawa, Canada.
David Kerr is a Professor at the Texas A&M University in College Station, TX, USA.
N. Christopher Phillips is a Professor at the University of Oregon in Eugene, OR, USA.
Andrew S. Toms is a Professor at the Purdue University in West Lafayette, IN, USA.
Content
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.