Sensitive group actions on regular curves of almost $\leq n$ order

Suhua Wang; Enhui Shi; Hui Xu; Zhiwen Xie

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arXiv · 2102.00401

Sensitive group actions on regular curves of almost $\leq n$ order

Suhua Wang·Enhui Shi·Hui Xu·Zhiwen Xie

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Abstract

Let $X$ be a regular curve and $n$ be a positive integer such that for every nonempty open set $U\subset X$, there is a nonempty connected open set $V\subset U$ with the cardinality $|\partial_X(V)|\leq n$. We show that if $X$ admits a sensitive action of a group $G$, then $G$ contains a free subsemigroup and the action has positive geometric entropy. As a corollary, $X$ admits no sensitive nilpotent group action.

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Suhua Wang, Enhui Shi, Hui Xu, Zhiwen Xie. 2021-01-31. Sensitive group actions on regular curves of almost $\leq n$ order. https://arxiv.org/abs/2102.00401

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