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...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/133322 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/133322 |
| Access Level: | acceso abierto |
| Palabra clave: | Čech homology Eigenvalues Adding machines Entropy Topología 1210.13 Dinámica Topológica |
| Sumario: | 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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