17 feb 2021 -- 14:30
Roma Tor Vergata (online)
Seminari PRIN2017 "Real and Complex Manifolds: Topology, Geometry and Holomorphic Dynamics"
Abstract.
A central object of interest when describing the dynamics of a holomorphic self-map of a complex manifold is the Fatou set of points with stable dynamical behaviour and its connected components. These Fatou components have been completely classified in dimension one. In dimension two, steady progress has been made in selected subclasses since the 1990s, but the picture is far from complete. In this talk, I give a brief introduction to local dynamics and the classification of Fatou components in dimension one. I then proceed to new types of dynamics and Fatou components in dimension two and present a construction of doubly connected components with parabolic dynamics for automorphisms of \mathbb{C}{2}.