Sensitivity, local stable/unstable sets and shadowing
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arXiv
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| Format: | Preprint |
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2020
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| author | Antunes, Mayara Carvalho, Bernardo Tacuri, Margoth |
| author_facet | Antunes, Mayara Carvalho, Bernardo Tacuri, Margoth |
| contents | In this paper we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets always contain a compact and perfect subset of the space. As a corollary we generalize results in [6] and [11] proving that positively countably expansive homeomorphisms defined on compact metric spaces satisfying either transitivity and the shadowing property, or the L-shadowing property, can only be defined in countably spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_08894 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Sensitivity, local stable/unstable sets and shadowing Antunes, Mayara Carvalho, Bernardo Tacuri, Margoth Dynamical Systems In this paper we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets always contain a compact and perfect subset of the space. As a corollary we generalize results in [6] and [11] proving that positively countably expansive homeomorphisms defined on compact metric spaces satisfying either transitivity and the shadowing property, or the L-shadowing property, can only be defined in countably spaces. |
| title | Sensitivity, local stable/unstable sets and shadowing |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2012.08894 |