On ball expanding maps
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909720309137408 |
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| author | Kawaguchi, Noriaki |
| author_facet | Kawaguchi, Noriaki |
| contents | We study the dynamical properties of ball expanding maps, a class of continuous self-maps defined on compact metric spaces. For a ball expanding map, we show that: (1) the set of periodic points is dense in the chain recurrent set; (2) if the topological entropy of the map is zero, then the chain recurrent set is finite; (3) the map has only finitely many chain components; (4) if the space is perfect, then the topological entropy of the map is positive; and (5) if the space is connected, then the map is locally eventually onto and hence mixing. Several examples are also provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04744 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On ball expanding maps Kawaguchi, Noriaki Dynamical Systems 37B05, 37B65 We study the dynamical properties of ball expanding maps, a class of continuous self-maps defined on compact metric spaces. For a ball expanding map, we show that: (1) the set of periodic points is dense in the chain recurrent set; (2) if the topological entropy of the map is zero, then the chain recurrent set is finite; (3) the map has only finitely many chain components; (4) if the space is perfect, then the topological entropy of the map is positive; and (5) if the space is connected, then the map is locally eventually onto and hence mixing. Several examples are also provided. |
| title | On ball expanding maps |
| topic | Dynamical Systems 37B05, 37B65 |
| url | https://arxiv.org/abs/2507.04744 |