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Gonzalo Cousillas

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Papers by Gonzalo Cousillas

Research paper thumbnail of Linearization of topologically Anosov homeomorphisms of non compact surfaces

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.

Research paper thumbnail of A fixed point theorem for Topologically Anosov Plane homeomorphisms

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.

Research paper thumbnail of Linearization of topologically Anosov homeomorphisms of non compact surfaces of genus zero and finite type

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}.

Research paper thumbnail of Generic Homeomorphisms with Shadowing of One-Dimensional Continua

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.

Research paper thumbnail of Topologically Anosov plane homeomorphisms

Topological Methods in Nonlinear Analysis, 2019

Research paper thumbnail of Linearization of topologically Anosov homeomorphisms of non compact surfaces

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.

Research paper thumbnail of A fixed point theorem for Topologically Anosov Plane homeomorphisms

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.

Research paper thumbnail of Linearization of topologically Anosov homeomorphisms of non compact surfaces of genus zero and finite type

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}.

Research paper thumbnail of Generic Homeomorphisms with Shadowing of One-Dimensional Continua

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.

Research paper thumbnail of Topologically Anosov plane homeomorphisms

Topological Methods in Nonlinear Analysis, 2019

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