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Title: On connectivity of Julia sets of transcendental meromorphic maps and weakly repelling fixed points I
Author: Fagella Rabionet, Núria
Jarque i Ribera, Xavier
Taixés i Ventosa, Jordi
Keywords: Sistemes dinàmics complexos
Funcions de variables complexes
Funcions meromorfes
Complex dynamical systems
Functions of complex variables
Meromorphic functions
Issue Date: 15-Apr-2008
Publisher: Oxford University Press
Abstract: 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.
Note: Versió postprint del document publicat a:
It is part of: Proceedings of the London Mathematical Society, 2008, vol. 97, num. 3, p. 599-622
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ISSN: 0024-6115
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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