Dynamics of Henon-type maps on C^k and theory of intersection of currents

2017/10/30 Mon 13:00 - 16:00
Dinh Tien Cuong
National University of Singapore

We will consider a large family of polynomial automorphisms of C^k which extends the family of Henon-type maps in dimension 2. After discussing some properties of Julia sets, Green currents, equilibrium measure, I will focus the talk on the equidistribution of periodic points. The proof requires a recent non-generic intersection theory for currents, possibly with dimension excess. It allows us to obtain an asymptotic non-transversality for the intersections between the graphs of the iterates of the map and the diagonal in (C^k)^2. This is crucial in the proof. Other applications of the intersection theory will be mentioned. The talk is based on my joint works with Nessim Sibony.