Equidistribution towards the Green current in complex dynamics

Abstract: Given a holomorphic self-map of complex projective space of de-gree larger than one, we prove that there exists a finite collection oftotally invariant algebraic sets with the following property: given anypositive closed (1,1)-current of mass 1 with no mass on any element of this family, the sequence of normalized pull-backs of the current converges to the Green current. Under suitable geometric conditions on the collection of totally invariant algebraic sets, we prove a sharper equidistribution result.