Topologically anosov plane homeomorphisms
Cousillas, Gonzalo (Universidad de la República (Uruguai). Instituto de Matemática y Estadística "Rafael Laguardia")
Groisman, Jorge (Universidad de la República (Uruguai). Instituto de Matemática y Estadística "Rafael Laguardia")
Xavier, Juliana (Universidad de la República (Uruguai). Instituto de Matemática y Estadística "Rafael Laguardia")

Date:	2019
Abstract:	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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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Topologically expansive homeomorphism ; Topological shadowing property ; Topologically Anosov plane homeomorphism ; Homothety
Published in:	Topological Methods in Nonlinear Analysis, Vol. 54, Issue 1 (September 2019) , p. 371-382, ISSN 1230-3429

DOI: 10.12775/TMNA.2019.050

Postprint 10 p, 330.8 KB

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