Para acceder a los documentos con el texto completo, por favor, siga el siguiente enlace: http://hdl.handle.net/2445/63074

On the Connectivity of the Julia sets of meromorphic functions
Baranski, Krzysztof; Fagella Rabionet, Núria; Jarque i Ribera, Xavier; Karpinska, Boguslava
Universitat de Barcelona
We prove that every transcendental meromorphic map $f$ with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.
Funcions enteres
Funcions de variables complexes
Entire functions
Functions of complex variables
(c) Springer Verlag, 2014
Artículo
info:eu-repo/semantics/acceptedVersion
Springer Verlag
         

Mostrar el registro completo del ítem

Documentos relacionados

Otros documentos del mismo autor/a

Devaney, Robert L.; Fagella Rabionet, Núria; Garijo Real, Antonio; Jarque i Ribera, Xavier
Devaney, Robert L.; Fagella Rabionet, Núria; Garijo Real, Antonio; Jarque i Ribera, Xavier
Fagella Rabionet, Núria; Godillon, Sébastien; Jarque i Ribera, Xavier