Speaker: Jamin Raissy (University of Bordeaux)
Title: Perturbations of parabolic endomorphisms in dimension 2
Abstract: In this talk, I will present a work in progress with Matthieu Astorg and Lorena Lopez-Hernanz. We are interested in studying holomorphic endomorphisms of $\mathbb{C}^2$ which are tangent to the identity at the origin, and our goal is to understand how the dynamics changes when we perturb such maps. In particular, we generalize previous results obtained by Bianchi and show a statement {\it à la Lavaurs} when the unperturbed map admits a parabolic basin centered at a characteristic direction, but it does not fix a complex line. I will briefly recall the motivation and results in the one-dimensional case before moving to dimension 2.