In this paper we give a unified proof of the fact that the Julia set ofNewton's method applied to a holomorphic function of the complex plane (apolynomial of degree large than $1$ or an entire transcendental function) isconnected. The result was recently completed by the authors' previous work, asa consequence of a more general theorem whose proof spreads among many papers,which consider separately a number of particular cases for rational andtranscendental maps, and use a variety of techniques. In this note we present aunified, direct and reasonably self-contained proof which works for allsituations alike.
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