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Minimal subdynamics and minimal flows without characteristic measures

Abstract

Given a countable group $G$ and a $G$-flow $X$, a measure $\mu\in P(X)$ is called characteristic if it is $\mathrm{Aut}(X, G)$-invariant. Frisch and Tamuz asked about the existence of a minimal $G$-flow, for any group $G$, which does not admit a characteristic measure. We construct for every countable group $G$ such a minimal flow. Along the way, we are motivated to consider a family of questions we refer to as minimal subdynamics: Given a countable group $G$ and a collection of infinite subgroups $\{\Delta_i: i\in I\}$, when is there a faithful $G$-flow for which every $\Delta_i$ acts minimally?

Dates and versions

hal-03960060 , version 1 (27-01-2023)

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Joshua Frisch, Brandon Seward, Andy Zucker. Minimal subdynamics and minimal flows without characteristic measures. 2023. ⟨hal-03960060⟩
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