Disjointness with all minimal systems under group actions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910560569786368 |
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| author | Xu, Hui Ye, Xiangdong |
| author_facet | Xu, Hui Ye, Xiangdong |
| contents | Let $G$ be a countable discrete group. We give a necessary and sufficient condition for a transitive $G$-system to be disjoint with all minimal $G$-systems, which implies that if a transitive $G$-system is disjoint with all minimal $G$-systems, then it is $\infty$-transitive, i.e. $(X^k,G)$ is transitive for all $k\in\N$, and has dense minimal points. In addition, we show that any $\infty$-transitive $G$-system with dense distal points are disjoint with all minimal $G$-systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_07830 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Disjointness with all minimal systems under group actions Xu, Hui Ye, Xiangdong Dynamical Systems 37B05 Let $G$ be a countable discrete group. We give a necessary and sufficient condition for a transitive $G$-system to be disjoint with all minimal $G$-systems, which implies that if a transitive $G$-system is disjoint with all minimal $G$-systems, then it is $\infty$-transitive, i.e. $(X^k,G)$ is transitive for all $k\in\N$, and has dense minimal points. In addition, we show that any $\infty$-transitive $G$-system with dense distal points are disjoint with all minimal $G$-systems. |
| title | Disjointness with all minimal systems under group actions |
| topic | Dynamical Systems 37B05 |
| url | https://arxiv.org/abs/2212.07830 |