Connectivity of Julia sets of Newton maps : a unified approach
Barański, Krzysztof (University of Warsaw (Polònia). 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 (University of Warsaw (Polònia). Institute of Mathematics)

Date:	2018
Abstract:	In this paper we give a unified proof of the fact that the Julia set of Newton's method applied to a holomorphic function of the complex plane (a polynomial of degree large than 1 or an entire transcendental function) is connected. The result was recently completed by the authors' previous work, as a consequence of a more general theorem whose proof spreads among many papers, which consider separately a number of particular cases for rational and transcendental maps, and use a variety of techniques. In this note we present a unified, direct and reasonably self-contained proof which works for all situations alike.
Grants:	Ministerio de Economía y Competitividad MTM2011-26995-C02-02 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-792
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Connectivity ; Fatou set ; Holomorphic dynamics ; Julia set ; Newton's map ; Repelling fixed point ; Simple connectivity
Published in:	Revista Matemática Iberoamericana, Vol. 34, issue 3 (2018) , p. 1211-1228, ISSN 0213-2230

DOI: 10.4171/RMI/1022

Postprint 15 p, 8.6 MB

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