Title:
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Connectivity of Julia sets of Newton maps: a unified approach
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Author:
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Baranski, Krzysztof; Fagella Rabionet, Núria; Jarque i Ribera, Xavier; Karpinska, Boguslawa
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Other authors:
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Universitat de Barcelona |
Abstract:
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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. |
Subject(s):
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-Funcions enteres -Sistemes dinàmics complexos -Superfícies de Riemann -Entire functions -Complex dynamical systems -Riemann surfaces |
Rights:
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(c) European Mathematical Society Publishing House, 2018
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Document type:
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Article Article - Accepted version |
Published by:
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European Mathematical Society Publishing House
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