Baranski, KrzysztofFagella Rabionet, NúriaJarque i Ribera, XavierKarpinska, Boguslawa2015-02-182015-02-182014-02-080020-9910https://hdl.handle.net/2445/63074We prove that every transcendental meromorphic map $f$ with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.46 p.application/pdfeng(c) Springer Verlag, 2014Funcions enteresFuncions de variables complexesEntire functionsFunctions of complex variablesinfo:eu-repo/semantics/article6336012015-02-18info:eu-repo/semantics/openAccess