rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Ergodic Theory
    sub title: Independence and Dichotomies
  name:
    name part: Kerr, David.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Li, Hanfeng.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXXIV, 431 p. online resource.
  abstract: 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.
  table of 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.
  note: by David Kerr, Hanfeng Li.
  subject:
    topic: Mathematics
  subject:
    topic: Group theory
  subject:
    topic: Dynamics
  subject:
    topic: Ergodic theory
  subject:
    topic: Functional analysis
  subject:
    topic: Mathematics
  subject:
    topic: Dynamical Systems and Ergodic Theory
  subject:
    topic: Group Theory and Generalizations
  subject:
    topic: Functional Analysis
  classification: QA313
  classification: 515.39
  classification: 515.48
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Monographs in Mathematics
  identifier: 9783319498478
  identifier: http://dx.doi.org/10.1007/978-3-319-49847-8
  record info:
    record creation date: 170209
    record change date: 20170209174040.0
    record identifier: 978-3-319-49847-8