Abstract:

It is known that the Julia set of the Newton&prime s method for a non-constant polynomial is connected (M. Shishikura, 1990). This is, in fact, a consequence of a much more general result that establishes the relationship between simple connectivity of Fatou components of rational maps and fixed points which are repelling or parabolic with multiplier 1. In this talk I will speak of Fatou components of transcendental moromorphic maps instead, and show results and work in progress towards the transcendental versions of Shishikura&prime s theorems.

(Joint work with N. Fagella & X. Jarque.)