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http://hdl.handle.net/2445/63074
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: http://dx.doi.org/10.1007/s00222-014-0504-5 |
It is part of: | Inventiones Mathematicae, 2014, vol. 198, num. 3, p. 591-636 |
URI: | http://hdl.handle.net/2445/63074 |
Related resource: | http://dx.doi.org/10.1007/s00222-014-0504-5 |
ISSN: | 0020-9910 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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