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arXiv · 2006.09601

Positive entropy implies chaos along any infinite sequence

Wen Huang·Jian Li·Xiangdong Ye
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Abstract

Let $G$ be an infinite countable discrete amenable group. For any $G$-action on a compact metric space $(X,\rho)$, it turns out that if the action has positive topological entropy, then for any sequence $\{s_i\}_{i=1}^{+\infty}$ with pairwise distinct elements in $G$ there exists a Cantor subset $K$ of $X$ which is Li-Yorke chaotic along this sequence, that is, for any two distinct points $x,y\in K$, one has \[\limsup_{i\to+\infty}\rho(s_i x,s_iy)>0,\ \text{and}\ \liminf_{i\to+\infty}\rho(s_ix,s_iy)=0.\]

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Wen Huang, Jian Li, Xiangdong Ye. 2020-06-17. Positive entropy implies chaos along any infinite sequence. https://doi.org/10.1090/mosc/315

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