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Open AccessArticle

A Note on Anosov Homeomorphisms

Departamento de Matemática y Estadística del Litoral, Universidad de la República, Gral. Rivera 1350, Salto 50000, Uruguay
Axioms 2019, 8(2), 54; https://doi.org/10.3390/axioms8020054
Received: 9 April 2019 / Revised: 25 April 2019 / Accepted: 29 April 2019 / Published: 1 May 2019
(This article belongs to the Special Issue Shadowing in Dynamical Systems)
For an α -expansive homeomorphism of a compact space we give an elementary proof of the following well-known result in topological dynamics: A sufficient condition for the homeomorphism to have the shadowing property is that it has the α -shadowing property for one-jump pseudo orbits (known as the local product structure property). The proof relies on a reformulation of the property of expansiveness in terms of the pseudo orbits of the system. View Full-Text
Keywords: shadowing property; expansive homeomorphism; pseudo orbit shadowing property; expansive homeomorphism; pseudo orbit
MDPI and ACS Style

Achigar, M. A Note on Anosov Homeomorphisms. Axioms 2019, 8, 54.

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