Restricted orbit equivalence for actions of discrete amenable groups
著者
書誌事項
Restricted orbit equivalence for actions of discrete amenable groups
Cambridge University Press, 2002
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注記
Includes bibliographical references (p. 196-198) and index
内容説明・目次
内容説明
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.
目次
- 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.
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