Value Distribution for Sequences of Rational Mappings and Complex Dynamics
Alexander Russakovskii and Bernard Shiffman
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 ${\mathbb P}^n$. We show, assuming a condition on the topological degree $\lambda$ of $P$, that there is a probability measure $\mu$ on ${\mathbb P}^n$ such that the discrete measures $\lambda^{-k}P_k^*\delta_w$ converge to $\mu$ for all $w\in{\mathbb P}^n$ outside a pluripolar set.