Shadowing and the basins of terminal chain components
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929719174234112 |
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| author | Kawaguchi, Noriaki |
| author_facet | Kawaguchi, Noriaki |
| contents | We provide an alternative view of some results in [1, 3, 11]. In particular, we prove that (1) if a continuous self-map of a compact metric space has the shadowing, then the union of the basins of terminal chain components is a dense $G_δ$-subset of the space; and (2) if a continuous self-map of a locally connected compact metric space has the shadowing, and if the chain recurrent set is totally disconnected, then the map is almost chain continuous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15129 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shadowing and the basins of terminal chain components Kawaguchi, Noriaki Dynamical Systems 37B65 We provide an alternative view of some results in [1, 3, 11]. In particular, we prove that (1) if a continuous self-map of a compact metric space has the shadowing, then the union of the basins of terminal chain components is a dense $G_δ$-subset of the space; and (2) if a continuous self-map of a locally connected compact metric space has the shadowing, and if the chain recurrent set is totally disconnected, then the map is almost chain continuous. |
| title | Shadowing and the basins of terminal chain components |
| topic | Dynamical Systems 37B65 |
| url | https://arxiv.org/abs/2402.15129 |