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2021 Linearization of topologically Anosov homeomorphisms of non compact surfaces of genus zero and finite type
Gonzalo Cousillas, Jorge Groisman, Juliana Xavier
Topol. Methods Nonlinear Anal. 58(1): 323-333 (2021). DOI: 10.12775/TMNA.2021.002

Abstract

We study the dynamics of homeomorphisms of non-compact surfaces. In the case of surfaces of genus zero and finite type, we classify them. We prove that if $f\colon S \to S$, is a Topologically Anosov homeomorphism where $S$ is a non-compact surface of genus zero and finite type, then $S= \mathbb{R}^2$ and $f$ is conjugate to a homothety or reverse homothety (depending on wether $f$ preserves or reverses orientation). A weaker version of this result was conjectured in [6].

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Gonzalo Cousillas. Jorge Groisman. Juliana Xavier. "Linearization of topologically Anosov homeomorphisms of non compact surfaces of genus zero and finite type." Topol. Methods Nonlinear Anal. 58 (1) 323 - 333, 2021. https://doi.org/10.12775/TMNA.2021.002

Information

Published: 2021
First available in Project Euclid: 21 September 2021

Digital Object Identifier: 10.12775/TMNA.2021.002

Rights: Copyright © 2021 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.58 • No. 1 • 2021
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