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...

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Detalles Bibliográficos
Autores: Cousillas, Gonzalo|||0000-0002-2386-6937, Groisman, Jorge|||0000-0002-3448-2955, Xavier, Juliana
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
Descripción
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).