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...
| Autores: | , |
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| 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 |
| 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. |
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