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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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BARANSKI, Krzysztof, FAGELLA RABIONET, Núria, JARQUE I RIBERA, Xavier, KARPINSKA, Boguslawa. Connectivity of Julia sets of Newton maps: a unified approach. _Revista Matematica Iberoamericana_. 2018. Vol. 34, núm. 3, pàgs. 1211-1228. [consulta: 23 de gener de 2026]. ISSN: 0213-2230. [Disponible a: https://hdl.handle.net/2445/125727]