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Title: On the Connectivity of the Julia sets of meromorphic functions
Author: Baranski, Krzysztof
Fagella Rabionet, Núria
Jarque i Ribera, Xavier
Karpinska, Boguslawa
Keywords: Funcions enteres
Funcions de variables complexes
Entire functions
Functions of complex variables
Issue Date: 8-Feb-2014
Publisher: Springer Verlag
Abstract: 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.
Note: Versió postprint del document publicat a:
It is part of: Inventiones Mathematicae, 2014, vol. 198, num. 3, p. 591-636
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ISSN: 0020-9910
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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