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Examples in the entropy theory of countable group actions

Part of: Ergodic theory

Published online by Cambridge University Press:  25 March 2019

LEWIS BOWEN
LEWIS BOWEN*
Affiliation:
University of Texas at Austin, Mathematics, 1 University Station C1200, Austin, Texas, 78712, USA email [email protected]
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Abstract

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.

Keywords

sofic groupentropyOrnstein theoryBenjamini–Schramm convergence

MSC classification

Primary: 37A35: Entropy and other invariants, isomorphism, classification
Type
Survey Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 10 , October 2020 , pp. 2593 - 2680
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Copyright
© Cambridge University Press, 2019

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