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arXiv · 1908.02930

Characteristic measures of symbolic dynamical systems

Joshua Frisch·Omer Tamuz
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Abstract

A probability measure is a characteristic measure of a topological dynamical system if it is invariant to the automorphism group of the system. We show that zero entropy shifts always admit characteristic measures. We use similar techniques to show that automorphism groups of minimal zero entropy shifts are sofic.

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Joshua Frisch, Omer Tamuz. 2019-08-08. Characteristic measures of symbolic dynamical systems. https://doi.org/10.1017/etds.2021.16

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