English

Value distribution for sequences of rational mappings and complex dynamics

Complex Variables 2009-09-25 v1 Dynamical Systems

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 PkP_k of a rational mapping PP of \PPn\PP^n. We show, assuming a condition on the topological degree λ\lambda of PP, that there is a probability measure μ\mu on \PPn\PP^n such that the discrete measures λkPkδw\lambda^{-k}P_k^*\delta_w converge to μ\mu for all w\PPnw\in\PP^n outside a pluripolar set.

Keywords

Cite

@article{arxiv.math/9604204,
  title  = {Value distribution for sequences of rational mappings and complex dynamics},
  author = {Alexander Russakovskii and Bernard Shiffman},
  journal= {arXiv preprint arXiv:math/9604204},
  year   = {2009}
}