Dynamics and eigenvalues in dimension zero
Loading...
Official URL
Full text at PDC
Publication date
2020
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Cambridge University Press
Citations
Exportar
Citation
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.
Abstract
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∗.