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Hernández Corbato, Luis Nieves Rivera, David Jesús Romero Ruiz Del Portal, Francisco Sánchez Gabites, Jaime Jorge 2026-02-26T09:46:14Z 2026-02-26T09:46:14Z 2020 Hernández-Corbato, L., Nieves-Rivera, D. J., Del Portal, F. R. R., & Sánchez-Gabites, J. J. Dynamics and eigenvalues in dimension zero. Ergod. Th. & Dynam. Sys. 2020 Jan 4;40(9): 2434-2452. 10.1017/etds.2018.139 https://hdl.handle.net/20.500.14352/133322 Let X be a compact, metric and totally disconnected space and let f : X → X be a continuous map. We relate the eigenvalues of f∗ : ˇH0(X; C) → ˇH0(X; 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 a classical inequality of Manning that bounds the entropy of f below by the spectral radius of f∗. eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 International Dynamics and eigenvalues in dimension zero journal article