Quasi-disjointness in topological dynamics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910270293540864 |
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| author | Xu, Hui Ye, Xiangdong |
| author_facet | Xu, Hui Ye, Xiangdong |
| contents | Motivated by Berg's notion of quasi-disjointness for ergodic systems, we introduce and investigate the concept of quasi-disjointness for minimal systems. Several equivalent characterizations are provided. We prove that quasi-disjointness is preserved under taking factors, proximal extensions, and group extensions. As a consequence, we establish that every minimal {\bf PI} system is quasi-disjoint from all minimal systems. In addition, some variant of quasi-disjointness, namely strong quasi-disjointness is also introduced and examined. Particularly, we prove that each {\bf AI} system is strongly quasi-disjoint from all minimal systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30066 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasi-disjointness in topological dynamics Xu, Hui Ye, Xiangdong Dynamical Systems Motivated by Berg's notion of quasi-disjointness for ergodic systems, we introduce and investigate the concept of quasi-disjointness for minimal systems. Several equivalent characterizations are provided. We prove that quasi-disjointness is preserved under taking factors, proximal extensions, and group extensions. As a consequence, we establish that every minimal {\bf PI} system is quasi-disjoint from all minimal systems. In addition, some variant of quasi-disjointness, namely strong quasi-disjointness is also introduced and examined. Particularly, we prove that each {\bf AI} system is strongly quasi-disjoint from all minimal systems. |
| title | Quasi-disjointness in topological dynamics |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2605.30066 |