Restricted Orbit Equivalence for Actions of Discrete Amenable Groups

by Janet Whalen Kammeyer, Daniel J. Rudolph

Overview

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.

Product Details

ISBN-13:	9780521183857
Publisher:	Cambridge University Press
Publication date:	02/17/2011
Series:	Cambridge Tracts in Mathematics , #146
Pages:	208
Product dimensions:	5.90(w) x 8.90(h) x 0.60(d)

Table of Contents

1. Preface; 2. Definitions and examples; 3. The Ornstein–Weiss machinery; 4. Copying lemmas; 5. m-entropy; 6. m-joinings; 7. The equivalence theorem; 8. Appendix.

Editorial Reviews

Review of the hardback: '… this profound book … gives an attractive overview and backward look at the restricted orbit equivalence theory for single transformations and other 'small' groups.' Zentralblatt für Mathematik

From the Publisher