Minimal topological actions do not determine the measurable orbit equivalence class

2006/08/25 by Elek, Gábor, Ceccherini-Silberstein, Tullio
#37A20 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0608629

Abstract

We construct a minimal topological action \wp of a non-amenable group on a Cantor set C, which is non-uniquely ergodic and furthermore there exist ergodic invariant measures μ₁ and μ₂ such that (\wp,C,μ₁) and (\wp,C,μ₂) are not orbit equivalent measurable equivalence relations.

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