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N-expansive homeomorphisms with the shadowing property

Carvalho, B. ; Cordeiro, W.

Journal of Differential Equations, 2016-09, Vol.261 (6), p.3734-3755 [Periódico revisado por pares]

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Título:
N-expansive homeomorphisms with the shadowing property
Autor: Carvalho, B. ; Cordeiro, W.
Assuntos: Expansive ; Limit shadowing ; n-expansive ; Shadowing ; Transitive
É parte de: Journal of Differential Equations, 2016-09, Vol.261 (6), p.3734-3755
Descrição: 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.
Editor: Elsevier Inc
Idioma: Inglês

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