%0 Journal Article
%A Hernández Corbato, Luis
%A Nieves Rivera, David Jesús
%A Romero Ruiz Del Portal, Francisco
%A Sánchez Gabites, Jaime Jorge
%T Dynamics and eigenvalues in dimension zero
%D 2020
%U https://hdl.handle.net/20.500.14352/133322
%X 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∗.
%~