Restricted Orbit Equivalence of Discrete Amenable Groups
Edition: 1st edition
Publisher: Cambridge University Press
Published: January 15, 2002
Language: eng
Format: Hardcover
Number of pages: 203
ISBN-13: 9780521807951
Subjects: Calculus & mathematical analysis; Groups & group theory; Topology; Mathematics; Integral Calculus; Science/Mathematics; Probability & Statistics - General; Measure-preserving transformat; Calculus; General; Mathematics / General; Entropy (Information theory); Topology - General; Geometry - Algebraic; Measure-preserving transformations
First sentence: The purpose of this work is to lift the notion of restricted orbit equivalence to the category of free and ergodic actions of discrete amenable groups.
Description: "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, the Kakutani equivalence theory and a host of others. By putting such restrictions in an axiomatic framework, a general approach is developed that encompasses all these examples simultaneously and gives insight into how to seek further applications.

The work is placed in the context of discrete amenable group actions where time is not required to be one-dimensional, making the results applicable to a much wider range of problems and examples."--BOOK JACKET.