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Dynamics and eigenvalues in dimension zero.
- Source :
- Ergodic Theory & Dynamical Systems; Sep2020, Vol. 40 Issue 9, p2434-2452, 19p
- Publication Year :
- 2020
-
Abstract
- Let $X$ be a compact, metric and totally disconnected space and let $f:X\rightarrow X$ be a continuous map. We relate the eigenvalues of $f_{\ast }:\check{H}_{0}(X;\mathbb{C})\rightarrow \check{H}_{0}(X;\mathbb{C})$ 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 a classical inequality of Manning that bounds the entropy of $f$ below by the spectral radius of $f_{\ast }$. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01433857
- Volume :
- 40
- Issue :
- 9
- Database :
- Complementary Index
- Journal :
- Ergodic Theory & Dynamical Systems
- Publication Type :
- Academic Journal
- Accession number :
- 144906150
- Full Text :
- https://doi.org/10.1017/etds.2018.139