On homeomorphisms with the two-sided limit shadowing property
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2014
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| _version_ | 1866909354577362944 |
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| author | Carvalho, Bernardo Kwietniak, Dominik |
| author_facet | Carvalho, Bernardo Kwietniak, Dominik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1402_0674 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | On homeomorphisms with the two-sided limit shadowing property Carvalho, Bernardo Kwietniak, Dominik Dynamical Systems General Topology 37D20 (primary) 37B10, 37B20 (secondary) 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. |
| title | On homeomorphisms with the two-sided limit shadowing property |
| topic | Dynamical Systems General Topology 37D20 (primary) 37B10, 37B20 (secondary) |
| url | https://arxiv.org/abs/1402.0674 |