Luis Hernández-Corbato

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math.DS2018

Dynamics and eigenvalues in dimension zero

Luis Hernández-Corbato, David Jesús Nieves-Rivera, Francisco R. Ruiz Del Portal +1

Let $X$ be a compact, metric and totally disconnected space and let $f : X \to X$ be a continuos map. We relate the eigenvalues of $f_{*}:\check{H}_{0}(X;\mathbb{C})\to\check{H}_{0}(X…

math.DS2018

Infinite series in cohomology: attractors and Conley index

Luis Hernández-Corbato, Francisco R. Ruiz del Portal, Jaime J. Sánchez-Gabites

In this paper we study the cohomological Conley index of arbitrary isolated invariant continua for continuous maps $f : U \subseteq R^{d} \to R^{d}$ by analyzing…

math.DS2016

An elementary proof of a Theorem by Matsumoto

Luis Hernandez-Corbato

Matsumoto proved in arXiv:1012.0981 that the prime end rotation numbers associated to an invariant annular continuum are contained in its rotation set. An alternative proof of this…

math.DS2016

Indices of fixed points not accumulated by periodic points

Luis Hernandez-Corbato

We prove that for every integer sequence $I$ satisfying Dold relations there exists a map $f : R^{d} \to R^{d}$ , $d \geq 2$ , such that $\mathrm{Per(f)} = \mathrm{Fix(f…

math.DS2016

Fixed point indices of planar continuous maps

Luis Hernandez-Corbato, Francisco R. Ruiz del Portal

We characterize the sequences of fixed point indices ${i (f^{n}, p)}_{n \geq 1}$ of fixed points that are isolated as an invariant set and continuous maps in the plane. In particular,…