Topologically anosov plane homeomorphisms
This paper deals with classifying the dynamics of topologically Anosov plane homeomorphisms. We prove that a topologically Anosov homeomorphism f: R2 → R2 is conjugate to a homothety if it is the time one map of a flow. We also obtain results for the cases when the nonwan- dering set of f reduces to...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:221358 |
| Acceso en línea: | https://ddd.uab.cat/record/221358 https://dx.doi.org/urn:doi:10.12775/TMNA.2019.050 |
| Access Level: | acceso abierto |
| Palabra clave: | Topologically expansive homeomorphism Topological shadowing property Topologically Anosov plane homeomorphism Homothety |
| Sumario: | This paper deals with classifying the dynamics of topologically Anosov plane homeomorphisms. We prove that a topologically Anosov homeomorphism f: R2 → R2 is conjugate to a homothety if it is the time one map of a flow. We also obtain results for the cases when the nonwan- dering set of f reduces to a fixed point, or if there exists an open, connected, simply connected proper subset U such that U ⊂ Int(f(U)), and such that ∪n ≥ 0fn(U) = R2.In the general case, we prove a structure theorem for the α-limits of orbits with empty ω-limit (or the ω-limits of orbits with empty α-limit). |
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