Baranski, KrzysztofFagella Rabionet, NúriaJarque i Ribera, XavierKarpinska, Boguslawa2018-10-302018-10-302018-08-270213-2230https://hdl.handle.net/2445/125727In 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.18 p.application/pdfeng(c) European Mathematical Society Publishing House, 2018Funcions enteresSistemes dinàmics complexosSuperfícies de RiemannEntire functionsComplex dynamical systemsRiemann surfacesinfo:eu-repo/semantics/article6697062018-10-30info:eu-repo/semantics/openAccess