Restricted Orbit Equivalence for Actions of Discrete Amenable Groups

Erscheinungsjahr 2012
ISBN: 978-0-521-80795-1
Verlag: Cambridge University Press

Buch, Englisch, Band 146, 208 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 496 g

Reihe: Cambridge Tracts in Mathematics

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 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.

Autoren/Hrsg.

Kammeyer, Janet Whalen

Rudolph, Daniel J.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Inhaltsverzeichnis

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.