Lowering topological entropy over subsets for amenable group actions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918309780258816 |
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| author | Wang, Xiaochen |
| author_facet | Wang, Xiaochen |
| contents | In this paper, we introduce the notions of lowerable, D-lowerable, P-lowerable, hereditarily lowerable, and hereditarily uniformly lowerable for countably infinite amenable group actions. We show that a system with finite entropy is lowerable, D-lowerable, and P-lowerable, and that asymptotic h-expansiveness is equivalent to hereditary uniform lowerability. Moreover, we prove a Bowen's type theorem for amenable group actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19613 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lowering topological entropy over subsets for amenable group actions Wang, Xiaochen Dynamical Systems In this paper, we introduce the notions of lowerable, D-lowerable, P-lowerable, hereditarily lowerable, and hereditarily uniformly lowerable for countably infinite amenable group actions. We show that a system with finite entropy is lowerable, D-lowerable, and P-lowerable, and that asymptotic h-expansiveness is equivalent to hereditary uniform lowerability. Moreover, we prove a Bowen's type theorem for amenable group actions. |
| title | Lowering topological entropy over subsets for amenable group actions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2510.19613 |