Speaker. Núria Fagella
Date. 27.09.22 at 2:00 pm
Abstract. We discuss the concept of structural stability in holomorphic families of meromorphic maps, in the spirit of the celebrated theorem of Mañé-Sad-Sullivan and Lyubich in the 1980’s for rational maps. We show that for functions with an essential singularity at infinity, a new type of bifurcation occurs which consists of periodic points disappearing to infinity. Nevertheless, under some finiteness conditions, we show that J-structurally stable maps are open and dense in the appropriate parameter space (of arbitrary dimension).
(Joint work with Matthieu Astorg and Anna Miriam Benini)