N-expansive homeomorphisms with the shadowing property
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866912076738330624 |
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| author | Carvalho, Bernardo Cordeiro, Welington |
| author_facet | Carvalho, Bernardo Cordeiro, Welington |
| contents | We discuss the dynamics of $n$-expansive homeomorphisms with the shadowing property defined on compact metric spaces. For every $n\in\mathbb{N}$, we exhibit an $n$-expansive homeomorphism, which is not $(n-1)$-expansive, has the shadowing property and admits an infinite number of chain-recurrent classes. We discuss some properties of the local stable (unstable) sets of $n$-expansive homeomorphisms with the shadowing property and use them to prove that some types of the limit shadowing property are present. This deals some direction to the problem of non-existence of topologically mixing $n$-expansive homeomorphisms that are not expansive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1604_00704 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | N-expansive homeomorphisms with the shadowing property Carvalho, Bernardo Cordeiro, Welington Dynamical Systems We discuss the dynamics of $n$-expansive homeomorphisms with the shadowing property defined on compact metric spaces. For every $n\in\mathbb{N}$, we exhibit an $n$-expansive homeomorphism, which is not $(n-1)$-expansive, has the shadowing property and admits an infinite number of chain-recurrent classes. We discuss some properties of the local stable (unstable) sets of $n$-expansive homeomorphisms with the shadowing property and use them to prove that some types of the limit shadowing property are present. This deals some direction to the problem of non-existence of topologically mixing $n$-expansive homeomorphisms that are not expansive. |
| title | N-expansive homeomorphisms with the shadowing property |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/1604.00704 |