| Résume | In one dimensional complex dynamics there are several natural classes of functions to study: polynomials, rational maps, entire transcendental maps and meromorphic maps. In the first, introductory part of the talk, we will outline the major differences between polynomial and transcendental dynamics: the presence of an essential singularity at infinity dramatically changes the dynamical scenario, creating new types of Fatou components (Baker and wandering domains) and changing the topology and geometry of the Julia set.
In the second, more specialized part of the talk, we will explain some new results on parameter spaces of meromorphic maps, obtained in a joint work with M. Astorg and N. Fagella. We will show that a celebrated theorem by Mane-Sad-Sullivan and Lyubich holds also in an appropriate meromorphic setting, despite a completely new type of bifurcation behaviour that can occur when periodic cycles escape to infinity. |
