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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.14205 |
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| _version_ | 1866909617463754752 |
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| author | Shao, Song Xu, Hui |
| author_facet | Shao, Song Xu, Hui |
| contents | In this paper, we develop several structure theorems concerning commuting transformations and minimal $\mathbb{R}$-flows. Specifically, we show that if $(X,S)$, $(X,T)$ are minimal systems with $S$ and $T$ being commutative, then they possess an identical higher-order regionally proximal relation. Consequently, both $(X, S)$ and $(X, T)$ share the same increasing sequence of pro-nilfactors. For minimal $\mathbb{R}$-flows, we introduce the concept of higher-order regionally proximal relations and nilfactors, and establish that nilfactors are characteristic factors for minimal $\mathbb{R}$-flows, up to almost one to one extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14205 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure theorems of commuting transformations and minimal $\mathbb{R}$-flows Shao, Song Xu, Hui Dynamical Systems In this paper, we develop several structure theorems concerning commuting transformations and minimal $\mathbb{R}$-flows. Specifically, we show that if $(X,S)$, $(X,T)$ are minimal systems with $S$ and $T$ being commutative, then they possess an identical higher-order regionally proximal relation. Consequently, both $(X, S)$ and $(X, T)$ share the same increasing sequence of pro-nilfactors. For minimal $\mathbb{R}$-flows, we introduce the concept of higher-order regionally proximal relations and nilfactors, and establish that nilfactors are characteristic factors for minimal $\mathbb{R}$-flows, up to almost one to one extensions. |
| title | Structure theorems of commuting transformations and minimal $\mathbb{R}$-flows |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2505.14205 |