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arXiv · 2202.12503

Pinsker $\sigma$-algebra Character and mean Li-Yorke chaos

Chunlin Liu·Rongzhong Xiao·Leiye Xu
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Abstract

Let $G$ be an infinite countable discrete amenable group. For any $G$-action on a compact metric space $X$, it is proved that for any sequence $(G_n)_{n\ge 1}$ consisting of non-empty finite subsets of $G$ with $\lim_{n\to \infty}|G_n|=\infty$, Pinsker $\sigma$-algebra is a characteristic factor for $(G_n)_{n\ge 1}$. As a consequence, for a class of $G$-topological dynamical systems, positive topological entropy implies mean Li-Yorke chaos along a class of sequences consisting of non-empty finite subsets of $G$.

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Chunlin Liu, Rongzhong Xiao, Leiye Xu. 2022-02-25. Pinsker $\sigma$-algebra Character and mean Li-Yorke chaos. https://doi.org/10.1007/s10884-024-10381-8

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