Disjointness with all minimal systems under group actions

2022/12/15 by Xu, Hui, Ye, Xiangdong
#37B05 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.07830

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 ∞-transitive, i.e. (X^k,G) is transitive for all k∈\N, and has dense minimal points. In addition, we show that any ∞-transitive G-system with dense distal points are disjoint with all minimal G-systems.

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