N-expansive homeomorphisms with the shadowing property
We discuss the dynamics of n-expansive homeomorphisms with the shadowing property defined on compact metric spaces. For every n∈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 so...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2016 |
| País: | Brasil |
| Recursos: | Universidade Federal de Viçosa (UFV) |
| Repositório: | LOCUS Repositório Institucional da UFV |
| Idioma: | inglês |
| OAI Identifier: | oai:locus.ufv.br:123456789/21533 |
| Acesso em linha: | https://doi.org/10.1016/j.jde.2016.06.003 http://www.locus.ufv.br/handle/123456789/21533 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Expansive n-expansive Shadowing Transitive Limit shadowing |
| Resumo: | We discuss the dynamics of n-expansive homeomorphisms with the shadowing property defined on compact metric spaces. For every n∈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. |
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