Value distribution for sequences of rational mappings and complex dynamics. (English) Zbl 0901.58023

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.


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
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