Hypercyclic composition operators on spaces of real analytic functions

We study the dynamical behaviour of composition operators C φ defined on spaces A(Ω) of real analytic functions on an open subset Ω of ℝ d. We characterize when such operators are topologically transitive, i.e. when for every pair of non-empty open sets there is an orbit intersecting both of them. M...

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Detalles Bibliográficos
Autores: Bonet Solves, José Antonio|||0000-0002-9096-6380, Domański, Paweł
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/40660
Acceso en línea:https://riunet.upv.es/handle/10251/40660
Access Level:acceso abierto
Palabra clave:Composition operarators
Hypercyclic operators
Spaces of real analytic functions
MATEMATICA APLICADA
Descripción
Sumario:We study the dynamical behaviour of composition operators C φ defined on spaces A(Ω) of real analytic functions on an open subset Ω of ℝ d. We characterize when such operators are topologically transitive, i.e. when for every pair of non-empty open sets there is an orbit intersecting both of them. Moreover, under mild assumptions on the composition operator, we investigate when it is sequentially hypercyclic, i.e., when it has a sequentially dense orbit. If φ is a self map on a simply connected complex neighbourhood U of ℝ, U ≠ ℂ, then topological transitivity, hypercyclicity and sequential hypercyclicity of C φ: A(ℝ) → A(ℝ) are equivalent. © 2012 Cambridge Philosophical Society.