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arXiv · 2203.04875

Minimal subdynamics and minimal flows without characteristic measures

Joshua Frisch·Brandon Seward·Andy Zucker
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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?

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Joshua Frisch, Brandon Seward, Andy Zucker. 2022-03-09. Minimal subdynamics and minimal flows without characteristic measures. https://doi.org/10.1017/fms.2024.41

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