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| Título: | Topologically Anosov plane homeomorphisms |
| Autor: | Cousillas, Gonzalo Groisman, Jorge Xavier, Juliana |
| Tipo: | Preprint |
| Palabras clave: | Topologically expansive homeomorphism, Topological shadowing property, Topologically Anosov plane homeomorphism, Homothety |
| Fecha de publicación: | 2018 |
| 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. |
| Citación: | Cousillas, G., Groisman, J. y Xavier, J. Topologically Anosov plane homeomorphisms [Preprint] Publicado en : arXiv:1805.02737v1 [math.DS], may. 2018, pp. 1-10, DOI: 10.48550/arXiv.1805.02737. https://arxiv.org/abs/1805.02737. |
| Licencia: | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| Aparece en las colecciones: | Publicaciones académicas y científicas - IMERL (Instituto de Matemática y Estadística Rafael Laguardia) |
Ficheros en este ítem:
| Fichero | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| CGX18.pdf | Preprint | 167,17 kB | Adobe PDF | Visualizar/Abrir |
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