Institute of Mathematics


Modul:   MAT760  Ergodic theory and dynamical systems seminar

Non-density of hyperbolicity in complex dynamics in several variables

Talk by Prof. Dr. Sébastien Biebler

Speaker invited by: Prof. Dr. Corinna Ulcigrai

Date: 17.04.24  Time: 13.30 - 14.30  Room: 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.