Singular values and non-repelling cycles for entire transcendental maps

Let $f$ be a map with bounded set of singular values for which periodic dynamic rays exist and land. We prove that each non-repelling cycle is associated to a singular orbit which cannot accumulate on any other non-repelling cycle. When $f$ has finitely many singular values this implies a refinement...

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Detalles Bibliográficos
Autores: Benini, Anna Miriam, Fagella Rabionet, Núria
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2020
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/172530
Acceso en línea:https://hdl.handle.net/2445/172530
Access Level:acceso abierto
Palabra clave:Sistemes dinàmics diferenciables
Funcions de variables complexes
Equacions funcionals
Differentiable dynamical systems
Functions of complex variables
Functional equations
Descripción
Sumario:Let $f$ be a map with bounded set of singular values for which periodic dynamic rays exist and land. We prove that each non-repelling cycle is associated to a singular orbit which cannot accumulate on any other non-repelling cycle. When $f$ has finitely many singular values this implies a refinement of the Fatou-Shishikura inequality.