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arXiv · 1807.08043

Dynamics and eigenvalues in dimension zero

Luis Hernández-Corbato·David Jesús Nieves-Rivera·Francisco R. Ruiz Del Portal·Jaime J. Sánchez-Gabites
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Abstract

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 $f_{*}:\check{H}_{0}(X;\mathbb{C})\to\check{H}_{0}(X;\mathbb{C})$ to dynamical properties of $f$, roughly showing that if the dynamics is complicated then every complex number of modulus different from 0,1 is an eigenvalue. This stands in contrast with the classical Manning's inequality.

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Luis Hernández-Corbato, David Jesús Nieves-Rivera, Francisco R. Ruiz Del Portal, Jaime J. Sánchez-Gabites. 2018-07-20. Dynamics and eigenvalues in dimension zero. https://doi.org/10.1017/etds.2018.139

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