Restricted Orbit Equivalence for Actions of Discrete Amenable Groups

by Janet Whalen Kammeyer , Daniel J. Rudolph

• ISBN13: 9780521807951
• ISBN10: 0521807956
• Format: Hardcover
• Copyright: 2002-05-06
• Publisher: Cambridge University Press

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