Dynamics and eigenvalues in dimension zero
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 e...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 2020 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/133322 |
| Online Access: | https://hdl.handle.net/20.500.14352/133322 |
| Access Level: | Open access |
| Keyword: | Čech homology Eigenvalues Adding machines Entropy Topología 1210.13 Dinámica Topológica |
| Summary: | 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∗. |
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