Value distribution for sequences of rational mappings and complex dynamics

Abstract

We obtain results on the asymptotic equidistribution of the pre-images of linear subspaces for sequences of rational mappings between projective spaces. As an application to complex dynamics, we consider the iterates $P_k$ of a rational mapping $P$ of $\PP^n$. We show, assuming a condition on the topological degree $λ$ of $P$, that there is a probability measure $μ$ on $\PP^n$ such that the discrete measures $λ^{-k}P_k^*δ_w$ converge to $μ$ for all $w\in\PP^n$ outside a pluripolar set.