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.
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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
Book Description
This monograph offers a broad investigative tool in ergodic theory and measurable dynamics. Themotivation 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.The authors develop a general approach and give insights into how to seek further applications. The work is placed in a context that makes the results applicable to a wide range of problems and examples.
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Inside This Book
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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. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
restricted orbit equivalence, rearrangement pair, metric compactification, amenable group actions, discrete amenable group, ergodic actions, reverse filtration, continuous involution, metric giving, residual subset, orbit joinings, conjugacy invariant, isomorphism theory, amenable groups, mean ergodic theorem, orbit relation, orbit equivalences, ergodic measures, free orbits, metrizable space, tower image, equivalence theory, finite partition, equal entropy, equivalence theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Polish G-action, Proof Let, Ornstein-Weiss Rokhlin, Proof Fix New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
restricted orbit equivalence, rearrangement pair, metric compactification, amenable group actions, discrete amenable group, ergodic actions, reverse filtration, continuous involution, metric giving, residual subset, orbit joinings, conjugacy invariant, isomorphism theory, amenable groups, mean ergodic theorem, orbit relation, orbit equivalences, ergodic measures, free orbits, metrizable space, tower image, equivalence theory, finite partition, equal entropy, equivalence theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Polish G-action, Proof Let, Ornstein-Weiss Rokhlin, Proof Fix New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 3
books:
- Ergodic Theory (Cambridge Studies in Advanced Mathematics) by Karl E. Petersen in Back Matter (1), and Back Matter (2)
- Ergodic Theory (Grundlehren der mathematischen Wissenschaften) by I. P. Kornfeld in Back Matter
- Restricted Orbit Equivalence (Memoirs of the American Mathematical Society) by Daniel J. Rudolph in Front Matter
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