On the connectivity of the Julia sets of meromorphic functions

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 sh...

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Bibliographic Details
Published in:	Inventiones mathematicae Vol. 198; no. 3; pp. 591 - 636
Main Authors:	Barański, Krzysztof, Fagella, Núria, Jarque, Xavier, Karpińska, Bogusława
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2014 Springer Nature B.V Springer Verlag
Subjects:	Absorption Boundaries Discs Disks Entire functions Funcions de variables complexes Funcions enteres Functions of complex variables Mathematical analysis Mathematics Mathematics and Statistics Meromorphic functions Newton methods Texts 30D20 Primary 30D05 37F10
ISSN:	0020-9910, 1432-1297
Online Access:	Get full text
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