9780521807951

Restricted Orbit Equivalence for Actions of Discrete Amenable Groups

by
  • ISBN13:

    9780521807951

  • ISBN10:

    0521807956

  • Format: Hardcover
  • Copyright: 2002-05-06
  • Publisher: Cambridge University Press
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Summary

This monograph offers a broad investigative tool in ergodic theory and measurable dynamics. The motivation for this work is that one may measure how similar two dynamical systems are by asking how much the time structure of orbits of one system must be distorted for it to become the other. Different restrictions on the allowed distortion will lead to different restricted orbit equivalence theories. These include Ornstein's Isomorphism theory, Kakutani Equivalence theory and a list of others. By putting such restrictions in an axiomatic framework, a general approach is developed that encompasses all of these examples simultaneously and gives insight into how to seek further applications.

Table of Contents

Introduction
1(12)
Overview
1(2)
A roadmap to the text
3(2)
History and references
5(6)
Directions for further Study
11(2)
Definitions and Examples
13(36)
Orbits, arrangements and rearrangements
13(7)
Definition of a size and m-equivalence
20(12)
Seven examples
32(17)
The Ornstein-Weiss Machinery
49(16)
Copying Lemmas
65(26)
m-entropy
91(9)
m-joinings
100(39)
Polish topologies
100(8)
Overview of the topology on m-joinings
107(1)
Modeling pairs of arrangements
108(5)
Modeling rearrangements
113(16)
Adding sizes to the picture
129(3)
More orbit joinings and m joinings
132(7)
The Equivalence Theorem
139(28)
Perturbing an m-equivalence
139(11)
The m-distance and m-finitely determined processes
150(11)
The equivalence theorem
161(6)
Appendix 167(29)
1-sizes
168(21)
p-sizes
189(7)
Bibliography 196(3)
Index 199

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