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Open AccessFeature PaperArticle

Zero Entropy Is Generic

Department of Mathematics, College of Natural Sciences, University of Texas at Austin, Austin, TX 78712, USA
Academic Editor: Tomasz Downarowicz
Entropy 2016, 18(6), 220;
Received: 16 April 2016 / Revised: 19 May 2016 / Accepted: 31 May 2016 / Published: 4 June 2016
(This article belongs to the Special Issue Entropic Properties of Dynamical Systems)
Dan Rudolph showed that for an amenable group, Γ, the generic measure-preserving action of Γ on a Lebesgue space has zero entropy. Here, this is extended to nonamenable groups. In fact, the proof shows that every action is a factor of a zero entropy action! This uses the strange phenomena that in the presence of nonamenability, entropy can increase under a factor map. The proof uses Seward’s recent generalization of Sinai’s Factor Theorem, the Gaboriau–Lyons result and my theorem that for every nonabelian free group, all Bernoulli shifts factor onto each other. View Full-Text
Keywords: entropy; measure-preserving actions entropy; measure-preserving actions
MDPI and ACS Style

Bowen, L. Zero Entropy Is Generic. Entropy 2016, 18, 220.

AMA Style

Bowen L. Zero Entropy Is Generic. Entropy. 2016; 18(6):220.

Chicago/Turabian Style

Bowen, Lewis. 2016. "Zero Entropy Is Generic" Entropy 18, no. 6: 220.

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