# name
Connectivity of Julia sets of Newton maps: a unified approach

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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.

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European Mathematical Society Publishing House

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Revista Matematica Iberoamericana, 2018, vol. 34, num. 3, p. 1211-1228

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(c) European Mathematical Society Publishing House, 2018

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Connectivity of Julia sets of Newton maps: a unified approach