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...

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Detalles Bibliográficos
Autores: Hernández Corbato, Luis, Nieves Rivera, David Jesús, Romero Ruiz Del Portal, Francisco, Sánchez Gabites, Jaime Jorge
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
Descripción
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∗.