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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.18231 |
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| _version_ | 1866917242601472000 |
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| author | Li, Jian Liang, Xianjuan Yang, Yini |
| author_facet | Li, Jian Liang, Xianjuan Yang, Yini |
| contents | Let $G$ be a countable infinite discrete group. We show that a subset $F$ of $G$ contains a return time set of some piecewise syndetic recurrent point $x$ in a compact Hausdorff space $X$ with a $G$-action if and only if $F$ is a quasi-central set. As an application, we show that if a nonempty closed subsemigroup $S$ of the Stone-Čech compactification $βG$ contains the smallest ideal $K(βG)$ of $βG$ then $S$-product recurrent is equivalent to distality, which partially answers a question of Auslander and Furstenberg (Trans. Amer. Math. Soc. 343, 1994, 221--232). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18231 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Return time sets and product recurrence Li, Jian Liang, Xianjuan Yang, Yini Dynamical Systems Let $G$ be a countable infinite discrete group. We show that a subset $F$ of $G$ contains a return time set of some piecewise syndetic recurrent point $x$ in a compact Hausdorff space $X$ with a $G$-action if and only if $F$ is a quasi-central set. As an application, we show that if a nonempty closed subsemigroup $S$ of the Stone-Čech compactification $βG$ contains the smallest ideal $K(βG)$ of $βG$ then $S$-product recurrent is equivalent to distality, which partially answers a question of Auslander and Furstenberg (Trans. Amer. Math. Soc. 343, 1994, 221--232). |
| title | Return time sets and product recurrence |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2406.18231 |