Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/125727
Title: | Connectivity of Julia sets of Newton maps: a unified approach |
Author: | Baranski, Krzysztof Fagella Rabionet, Núria Jarque i Ribera, Xavier Karpinska, Boguslawa |
Keywords: | Funcions enteres Sistemes dinàmics complexos Superfícies de Riemann Entire functions Complex dynamical systems Riemann surfaces |
Issue Date: | 27-Aug-2018 |
Publisher: | European Mathematical Society Publishing House |
Abstract: | In this paper we present a unified proof of the fact that the Julia set of Newton's method applied to a holomorphic function on the complex plane (a polynomial of degree larger than $1$ or a transcendental entire 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 in all situations alike. |
Note: | Versió postprint del document publicat a: https://doi.org/10.4171/RMI/1022 |
It is part of: | Revista Matematica Iberoamericana, 2018, vol. 34, num. 3, p. 1211-1228 |
URI: | http://hdl.handle.net/2445/125727 |
Related resource: | https://doi.org/10.4171/RMI/1022 |
ISSN: | 0213-2230 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
669706.pdf | 8.78 MB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.