Restricted Orbit Equivalence for Actions of Discrete Amenable Groups

This 2002 title offers a broad investigative tool in ergodic theory and measurable dynamics.

Janet Whalen Kammeyer (Author), Daniel J. Rudolph (Author)

9780521183857, Cambridge University Press

Paperback, published 17 February 2011

208 pages
22.9 x 15.2 x 1.2 cm, 0.31 kg

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

This 2002 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 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.

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.

Subject Areas: Calculus & mathematical analysis [PBK]