Minimal topological actions do not determine the measurable orbit equivalence class

Mathematics – Dynamical Systems

Scientific paper

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Scientific paper

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 $\mu_1$ and $\mu_2$ such that $(\wp,C,\mu_1)$ and
$(\wp,C,\mu_2)$ are not orbit equivalent measurable equivalence relations.

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