Sep 27, 2022
Structural stability in complex dynamics
Date: September 27, 2022 |
10:00 am –
Speaker: Núria Fagella, Universitat de Barcelona and Centre de Recerca Matemàtica (CRM)
Location: Heinzel Seminar Room / Office Bldg West (I21.EG.101)
We discuss the concept of structural stability in holomorphic families of meromorphic maps, in the spirit of the celebrated theorem of Ma-Sad-Sullivan and Lyubich in the 1980s 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)