Topologically Anosov plane homeomorphisms
Resumen:
This paper deals with classifying the dynamics of Topologically Anosov plane homeomorphisms. We prove that a Topologically Anosov home- omorphism 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 nonwandering 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≥0f n(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), and we show that any basin of attraction (or repulsion) must be unbounded.
| 2018 | |
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Topologically expansive homeomorphism Topological shadowing property Topologically Anosov plane homeomorphism Homothety |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/54924 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
