On homeomorphisms with the two-sided limit shadowing property |
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Authors: | Bernardo Carvalho Dominik Kwietniak |
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Institution: | 1. Universidade Federal do Rio de Janeiro – UFRJ, Brazil;2. Faculty of Mathematics and Computer Science, Jagiellonian University in Kraków, Poland |
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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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Keywords: | Pseudo-orbit Shadowing Limit shadowing Transitivity |
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