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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.03848 |
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| _version_ | 1866929325042827264 |
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| author | Dai, Xiongping |
| author_facet | Dai, Xiongping |
| contents | Let $H$ be a subnormal co-compact closed subgroup of a Hausdorff topological group $T$ and $X$ a compact Hausdorff space. We prove the inheritance theorem: A point of $X$ is almost periodic (a.p.) for $T\curvearrowright X$ iff it is a.p. for $H\curvearrowright X$. Moreover, if $T\curvearrowright X$ is minimal with $H\lhd T$, then $\mathscr{O}_H\colon X\rightarrow2^X$, ${x\mapsto\overline{Hx}}$ is a continuous mapping, and, $T\curvearrowright X/H$ is an a.p. nontrivial factor of $T\curvearrowright X$ iff $T\curvearrowright X\times T/H$ is not minimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03848 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On sncc-inheritance of pointwise almost periodicity in flows Dai, Xiongping Dynamical Systems 37B05, 54H15 Let $H$ be a subnormal co-compact closed subgroup of a Hausdorff topological group $T$ and $X$ a compact Hausdorff space. We prove the inheritance theorem: A point of $X$ is almost periodic (a.p.) for $T\curvearrowright X$ iff it is a.p. for $H\curvearrowright X$. Moreover, if $T\curvearrowright X$ is minimal with $H\lhd T$, then $\mathscr{O}_H\colon X\rightarrow2^X$, ${x\mapsto\overline{Hx}}$ is a continuous mapping, and, $T\curvearrowright X/H$ is an a.p. nontrivial factor of $T\curvearrowright X$ iff $T\curvearrowright X\times T/H$ is not minimal. |
| title | On sncc-inheritance of pointwise almost periodicity in flows |
| topic | Dynamical Systems 37B05, 54H15 |
| url | https://arxiv.org/abs/2404.03848 |