Disjointness with all minimal systems under group actions

Hui Xu; Xiangdong Ye

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arXiv · 2212.07830

Disjointness with all minimal systems under group actions

Hui Xu·Xiangdong Ye

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Abstract

Let $G$ be a countable discrete group. We give a necessary and sufficient condition for a transitive $G$-system to be disjoint with all minimal $G$-systems, which implies that if a transitive $G$-system is disjoint with all minimal $G$-systems, then it is $\infty$-transitive, i.e. $(X^k,G)$ is transitive for all $k\in\N$, and has dense minimal points. In addition, we show that any $\infty$-transitive $G$-system with dense distal points are disjoint with all minimal $G$-systems.

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Hui Xu, Xiangdong Ye. 2022-12-15. Disjointness with all minimal systems under group actions. https://arxiv.org/abs/2212.07830

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