Restricted Orbit Equivalence for Actions of Discrete Amenable Groups

ISBN-13: 9780521807951 / Angielski / Twarda / 2002 / 208 str.

Janet Whalen Kammeyer; Daniel Rudolph; Daniel J. Rudolph

Opis

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.

Recenzje

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

Spis treści

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.