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arXiv · 1402.0674

On homeomorphisms with the two-sided limit shadowing property

Bernardo Carvalho·Dominik Kwietniak
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Abstract

We prove that the two-sided limit shadowing property is among the strongest known notions of pseudo-orbit tracing. It implies shadowing, average shadowing, asymptotic average shadowing and specification properties. We also introduce a weaker notion that is called two-sided limit shadowing with a gap and prove that it implies shadowing and transitivity. We show that those two properties allow to characterize topological transitivity and mixing in a class of expansive homeomorphisms and hence they characterize transitive (mixing) shifts of finite type.

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Bernardo Carvalho, Dominik Kwietniak. 2014-02-04. On homeomorphisms with the two-sided limit shadowing property. https://doi.org/10.1016/j.jmaa.2014.06.011

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