Non-density of hyperbolicity in complex dynamics in several variables
Vortrag von Prof. Dr. Sébastien Biebler
Sprecher eingeladen von: Prof. Dr. Corinna Ulcigrai
Datum: 17.04.24 Zeit: 13.30 - 14.30 Raum: ETH HG G 19.1
One of the main goals in the theory of dynamical systems is to describe the dynamics of a "typical" map. For instance, in the case of diffeomorphisms of a given manifold, it was conjectured by Smale in the 60s that uniform hyperbolicity was generically satisfied. This hope was however fast discouraged by exhibiting dynamical systems displaying in a robust way dynamical configurations which are obstructions to hyperbolicity: robust homoclinic tangencies (this is the so-called Newhouse phenomenon) and robust heterodimensional cycles. In this talk, I will explain these phenomena and their extensions to the complex setting. In particular, I will show how to construct robust heterodimensional cycles in the family of polynomial automorphisms of C^3. The main tool is the notion of blender coming from real dynamics.