Anna Miriam Benini (Università di Parma)

Abstract: In this talk we explore families of meromorphic maps which  are parametrized by finite dimensional  complex manifolds. We look at  such families from the point of view of how the dynamics of each single map varies when the parameter changes in the family. A map  is stable if all maps in a neighborhood of it have similar dynamics in a precise sense; it is a bifurcation parameter otherwise. 
In the first part of the talk we  present the problem, and several results concerning bifurcations and stability in natural families of meromorphic maps. This allows to  conclude that stable maps are dense in appropriate families. In the second part, we explain more about the structure of such parameter spaces, and some of the analytic and geometric tools which are involved in the study of such parameters.
This is joint work with M. Astorg and  N. Fagella. It extends to meromorphic maps  classical results proven by Lyubich,  Mane-Sad-Sullivan, and Eremenko-Lyubich for rational and entire maps, by dealing with a completely new type of bifurcations which only occurs in the meromorphic setting.