Pinsker $σ$-algebra Character and mean Li-Yorke chaos
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916364477792256 |
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| author | Liu, Chunlin Xiao, Rongzhong Xu, Leiye |
| author_facet | Liu, Chunlin Xiao, Rongzhong Xu, Leiye |
| contents | 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 $σ$-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 $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_12503 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pinsker $σ$-algebra Character and mean Li-Yorke chaos Liu, Chunlin Xiao, Rongzhong Xu, Leiye Dynamical Systems 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 $σ$-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 $G$. |
| title | Pinsker $σ$-algebra Character and mean Li-Yorke chaos |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2202.12503 |