Simons Semester in Banach Center: "Dynamical Systems"

Francois Berteloot: Bifurcations, Currents and Equidistribution phenomena in holomorphic dynamics

François Berteloot (Université Paul Sabatier, Toulouse)

Bifurcations, Currents and Equidistribution phenomena in holomorphic dynamics

8x45min

Abstract:

This course is based on the use of pluripotential theory, and in particular of bifurcation currents, to study holomorphic families of mappings.  Its aim is twofold. On one hand, we shall see how  to recover the classical Mane-Sad-Sullivan theory about bifurcations within holomorphic families of rational maps on the Riemann sphere and how to extend it to  families of endomorphisms of higher dimensional projective spaces. On the other hand, we shall discuss various equidistribution phenomena towards the bifurcation current or its self-powers, in parameter spaces.