Rigid actions have zero entropy

Lewis Bowen

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arXiv · 1507.07981

Rigid actions have zero entropy

Lewis Bowen

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Abstract

Rigid actions have zero Rokhlin entropy and nonpositive sofic entropy. Because rigidity is a stable orbit-equivalence invariant, this provides the first example of an essentially free, ergodic, probability-measure-preserving action of the free group that has nonpositive sofic entropy and any essentially free action stably-orbit-equivalent to it also has nonpositive sofic entropy.

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Lewis Bowen. 2015-07-30. Rigid actions have zero entropy. https://arxiv.org/abs/1507.07981

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