Rigid actions have zero entropy
Dynamical Systems
2015-07-31 v2 Operator Algebras
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.
Cite
@article{arxiv.1507.07981,
title = {Rigid actions have zero entropy},
author = {Lewis Bowen},
journal= {arXiv preprint arXiv:1507.07981},
year = {2015}
}
Comments
This paper was been withdrawn due to an error in the proof. Specifically, Lemma 4.3 is incorrect. See Ioana-Vaes's paper for a counterexample