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arXiv · 1904.04490

A note on Anosov homeomorphisms

Mauricio Achigar
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Abstract

For an $\alpha$-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 $\alpha$-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.

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Mauricio Achigar. 2019-04-09. A note on Anosov homeomorphisms. https://arxiv.org/abs/1904.04490

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