Beyond topological hyperbolicity: the L-shadowing property
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2019
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| _version_ | 1866909354589945856 |
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| author | Artigue, A. Carvalho, B. Cordeiro, W. Vieitez, J. |
| author_facet | Artigue, A. Carvalho, B. Cordeiro, W. Vieitez, J. |
| contents | In this paper we further explore the L-shadowing property defined in [17] for dynamical systems on compact spaces. We prove that structurally stable diffeomorphisms and some pseudo-Anosov diffeomorphisms of the two-dimensional sphere satisfy this property. Homeomorphisms satisfying the L-shadowing property have a spectral decomposition where the basic sets are either expansive or contain arbitrarily small topological semi-horseshoes (periodic sets where the restriction is semiconjugate to a shift). To this end, we characterize the L-shadowing property using local stable and unstable sets and the classical shadowing property. We exhibit homeomorphisms with the L-shadowing property and arbitrarily small topological semi-horseshoes without periodic points. At the end, we show that positive finite-expansivity jointly with the shadowing property imply that the space is finite. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1902_07578 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Beyond topological hyperbolicity: the L-shadowing property Artigue, A. Carvalho, B. Cordeiro, W. Vieitez, J. Dynamical Systems 37C50, 37B40, 37D20 In this paper we further explore the L-shadowing property defined in [17] for dynamical systems on compact spaces. We prove that structurally stable diffeomorphisms and some pseudo-Anosov diffeomorphisms of the two-dimensional sphere satisfy this property. Homeomorphisms satisfying the L-shadowing property have a spectral decomposition where the basic sets are either expansive or contain arbitrarily small topological semi-horseshoes (periodic sets where the restriction is semiconjugate to a shift). To this end, we characterize the L-shadowing property using local stable and unstable sets and the classical shadowing property. We exhibit homeomorphisms with the L-shadowing property and arbitrarily small topological semi-horseshoes without periodic points. At the end, we show that positive finite-expansivity jointly with the shadowing property imply that the space is finite. |
| title | Beyond topological hyperbolicity: the L-shadowing property |
| topic | Dynamical Systems 37C50, 37B40, 37D20 |
| url | https://arxiv.org/abs/1902.07578 |