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arXiv · 2110.01112

Existence of asymptotic pairs in positive entropy group actions

Mateusz Więcek
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Abstract

We provide a definition of a $\prec$-asymptotic pair in a topological action of a countable amenable group $G$, where $\prec$ is an order on $G$ of type $\mathbb Z$. We then prove that if $(\tilde{\mathcal O},\nu,G)$ is a multiorder on $G$, then for every topological $G$-action of positive entropy there exists an $\prec$-asympotic pair for almost every order $\prec\,\in\tilde{\mathcal O}$. This result is a generalization of the Blanchard-Host-Ruette Theorem for classical topological dynamical systems (actions of $\mathbb Z$).

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Mateusz Więcek. 2021-10-03. Existence of asymptotic pairs in positive entropy group actions. https://arxiv.org/abs/2110.01112

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