Open AccessLinearization of topologically Anosov homeomorphisms of non compact surfaces of genus zero and finite type
Author(s) -
Gonzalo Cousillas,
Jorge Groisman,
Juliana Xavier
Publication year - 2021
Publication title -
topological methods in nonlinear analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.623
H-Index - 23
ISSN - 1230-3429
DOI - 10.12775/tmna.2021.002
Subject(s) - mathematics , homothetic transformation , genus , zero (linguistics) , topological conjugacy , type (biology) , homeomorphism (graph theory) , pure mathematics , surface (topology) , combinatorics , geometry , ecology , linguistics , philosophy , botany , biology
We study the dynamics of {\it topologically Anosov} 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 \cite{cgx}.