## 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.

### 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
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