VALUE DISTRIBUTION FOR SEQUENCES OF RATIONAL MAPPINGS AND COMPLEX DYNAMICS

ALEXANDER RUSSAKOVSKII BERNARD SHIFFMAN

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 ℙ^{n}. We show, assuming a condition on the topological degree λ of P, that there is a probability measure μ on ℙ^{n} such that the discrete measures λ^{−k}P_{k}^{∗}δ_{w} converge to μ for all w ∈ ℙ^{n} outside a pluripolar set.