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...

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Detalhes bibliográficos
Autores: Carvalho, B., Cordeiro, W.
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
Descrição
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.