Russakovskii, Alexander; Shiffman, Bernard Value distribution for sequences of rational mappings and complex dynamics. (English) Zbl 0901.58023 Indiana Univ. Math. J. 46, No. 3, 897-932 (1997). We study pre-images under the iterates \(P^k\) of a rational (not necessarily holomorphic) 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 \(\mathbb{P}^n\) and a pluripolar set \({\mathcal E} \subset \mathbb{P}^n\) such that \(\lambda^{-k} P^{k*} \nu\to \mu\) for all probability measures \(\nu\) on \(\mathbb{P}^n \setminus {\mathcal E}\). We also obtain results on the asymptotic equidistribution of the preimages of linear subspaces for sequences of rational mappings between projective spaces. Reviewer: Bernard Shiffman (Baltimore) Cited in 55 Documents MSC: 37B99 Topological dynamics 30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable 37F99 Dynamical systems over complex numbers Keywords:complex dynamics; rational map; equidistribution; proximity function; plurisubharmonic function; positive current; Green function; Levine current; Fatou set; iteration; probability measure PDF BibTeX XML Cite \textit{A. Russakovskii} and \textit{B. Shiffman}, Indiana Univ. Math. J. 46, No. 3, 897--932 (1997; Zbl 0901.58023) Full Text: DOI arXiv Link OpenURL