On connectivity of Julia sets of transcendental meromorphic maps and weakly repelling fixed points I

It is known that the Julia set of the Newton's method of a non- constant polynomial is connected ([18]). This is, in fact, a consequence of a much more general result that establishes the relationship between simple connectivity of Fatou components of rational maps and fixed points which are re...

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Detalles Bibliográficos
Autores: Fagella Rabionet, Núria, Jarque i Ribera, Xavier, Taixés i Ventosa, Jordi
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2008
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/164190
Acceso en línea:https://hdl.handle.net/2445/164190
Access Level:acceso abierto
Palabra clave:Sistemes dinàmics complexos
Funcions de variables complexes
Funcions meromorfes
Complex dynamical systems
Functions of complex variables
Meromorphic functions
Descripción
Sumario:It is known that the Julia set of the Newton's method of a non- constant polynomial is connected ([18]). This is, in fact, a consequence of a much more general result that establishes the relationship between simple connectivity of Fatou components of rational maps and fixed points which are repelling or parabolic with multiplier 1. In this paper we study Fatou components of transcendental mero- morphic functions, namely, we show the existence of such fixed points provided that immediate attractive basins or preperiodic components be multiply connected.