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34 p, 476.4 KB On the connectivity of Julia sets of meromorphic functions / Barański, Krzysztof (University of Warsaw(Poland). Institute of Mathematics) ; Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ; Karpinska, Boguslawa (Warsaw University of Technology(Poland). Faculty of Mathematics and Information Science)
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. [...]
2014 - 10.1007/s00222-014-0504-5
Inventiones Mathematicae, Vol. 198 Núm. 3 (2014) , p. 591-636  
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