Various shadowing properties and their equivalence

By Keonhee Lee, Kazuhiro Sakai. 2005

76 citations recorded by the source corpus.

In this paper, various shadowing properties are considered for expansive homeomorphisms. More precisely, we show that the continuous shadowing property, the Lipschitz shadowing property, the limit shadowing property and the strong shadowing property are all equivalent to the (usual) shadowing property for expansive homeomorphisms on compact metric spaces.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7324d75e873a935e3833e84f50c24cd6aa029453

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On almost specification and average shadowing properties (2013, background): “By the above facts, we can extend results of [20] to a complete characterization of shadowing in expansive systems.”
On homeomorphisms with the two-sided limit shadowing property (2014, background): “5], where limit shadowing of [9] appears as s-limit shadowing).”
Shadowing and $\omega $-limit sets of circular Julia sets (2011, background): “The definition of limit shadowing was extended in [17] to a property called s-limit shadowing (Definition 3.”