Zero-dimensional extensions of amenable group actions

2015/03/10 by Huczek, Dawid
#37A35 #37B40 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.02827

Abstract

We prove that every dynamical system X with free action of a countable amenable group G by homeomorphisms has a zero-dimensional extension Y which is faithful and principal, i.e. every G-invariant measure μ on X has exactly one preimage ν on Y and the conditional entropy of ν with respect to X is zero. This is a version of an earlier result by T. Downarowicz and D. Huczek, which establishes the existence of zero-dimensional principal and faithful extensions for general actions of the group of integers.

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