Examples in the entropy theory of countable group actions

Kolmogorov–Sinai entropy is an invariant of measure-preserving actions of the group of integers that is central to classification theory. There are two recently developed invariants, sofic entropy and Rokhlin entropy, that generalize classical entropy to actions of countable groups. These new theori...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2020-10, Vol.40 (10), p.2593-2680
Main Author: BOWEN, LEWIS
Format: Article
Language:English
Subjects:
Entropy
Invariants
Survey Article
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Summary:Kolmogorov–Sinai entropy is an invariant of measure-preserving actions of the group of integers that is central to classification theory. There are two recently developed invariants, sofic entropy and Rokhlin entropy, that generalize classical entropy to actions of countable groups. These new theories have counterintuitive properties such as factor maps that increase entropy. This survey article focusses on examples, many of which have not appeared before, that highlight the differences and similarities with classical theory.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2019.18