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Papers by Gonzalo Cousillas
We study the dynamics of Topologically Anosov homeomorphisms of non compact surfaces. In the case... more We study the dynamics of 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:S → S, is a Topologically Anosov homeomorphism where S is a non-compact surface of genus zero and finite type, then S= ^ 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 a previous work.
arXiv: Dynamical Systems, 2018
Certain notions of expansivity and shadowing were defined on topological spaces which are dynamic... more Certain notions of expansivity and shadowing were defined on topological spaces which are dynamical properties and generalize the usual definitions. A Topologically Anosov homeomorphism is a homeomorphism with such properties. We exhibit explicit examples of Topologically Anosov homeomorphisms on the plane. Our main result is a fixed point theorem for orientation preserving Topologically Anosov plane homeomorphisms.
Topological Methods in Nonlinear Analysis, 2021
We study the dynamics of {\it topologically Anosov} homeomorphisms of non-compact surfaces. In th... more 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 fcolonStoSf\colon S \to SfcolonStoS, is a Topologically Anosov homeomorphism where SSS is a non-compact surface of genus zero and finite type, then S=mathbbR2S= \mathbb{R}^2S=mathbbR2 and fff is conjugate to a homothety or reverse homothety (depending on wether fff preserves or reverses orientation). A weaker version of this result was conjectured in \cite{cgx}.
Axioms, 2019
In this article, we show that there are homeomorphisms of plane continua whose conjugacy class is... more In this article, we show that there are homeomorphisms of plane continua whose conjugacy class is residual and have the shadowing property.
Topological Methods in Nonlinear Analysis, 2019
We study the dynamics of Topologically Anosov homeomorphisms of non compact surfaces. In the case... more We study the dynamics of 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:S → S, is a Topologically Anosov homeomorphism where S is a non-compact surface of genus zero and finite type, then S= ^ 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 a previous work.
arXiv: Dynamical Systems, 2018
Certain notions of expansivity and shadowing were defined on topological spaces which are dynamic... more Certain notions of expansivity and shadowing were defined on topological spaces which are dynamical properties and generalize the usual definitions. A Topologically Anosov homeomorphism is a homeomorphism with such properties. We exhibit explicit examples of Topologically Anosov homeomorphisms on the plane. Our main result is a fixed point theorem for orientation preserving Topologically Anosov plane homeomorphisms.
Topological Methods in Nonlinear Analysis, 2021
We study the dynamics of {\it topologically Anosov} homeomorphisms of non-compact surfaces. In th... more 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 fcolonStoSf\colon S \to SfcolonStoS, is a Topologically Anosov homeomorphism where SSS is a non-compact surface of genus zero and finite type, then S=mathbbR2S= \mathbb{R}^2S=mathbbR2 and fff is conjugate to a homothety or reverse homothety (depending on wether fff preserves or reverses orientation). A weaker version of this result was conjectured in \cite{cgx}.
Axioms, 2019
In this article, we show that there are homeomorphisms of plane continua whose conjugacy class is... more In this article, we show that there are homeomorphisms of plane continua whose conjugacy class is residual and have the shadowing property.
Topological Methods in Nonlinear Analysis, 2019