Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Entropy and actions of sofic groups

Pages: 3375 - 3383, Volume 20, Issue 10, December 2015      doi:10.3934/dcdsb.2015.20.3375

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Benjamin Weiss - Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel (email)

Abstract: In recent years there has been a great deal of progress in the study of actions of countable groups. In particular, the concept of the entropy of an action has been extended to all sofic groups following the seminal work of Lewis Bowen. This survey is an invitation to these new developments. It includes a new proof of the analogue of Kolmogorov's theorem for sofic groups, namely that isomorphic Bernoulli shifts have the same base entropy.

Keywords:  Entropy, amenable groups, sofic groups, Bernoulli shifts, Kolmogorov's theorem.
Mathematics Subject Classification:  Primary: 37A15, 31A35; Secondary: 22F10.

Received: February 2015;      Revised: February 2015;      Available Online: September 2015.