On homeomorphisms with the two-sided limit shadowing property

By B. Carvalho, Dominik Kwietniak. 2014

46 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c21f5b0396c55a304583e5f5791802dd1a8ced3e

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In Mathematical Physics

1. B. Carvalho
2. W. Cordeiro

Citations in the corpus

• N-expansive homeomorphisms with the shadowing property (2016, background): “dowing property then it has the limit shadowing property. If, in addition, it is topologically mixing, then it has the two-sided limit shadowing property. These results generalize Theorems C and D in [8] to the n-expansive scenario and gives some direction to the following question: Question 1. Does”