Distribution des preimages et des points periodiques d'une correspondance polynomiale

Abstract

We construct an equilibrium measure $μ$ for a polynomial correspondence F of Lojasiewicz exponent l>1. We then show that $μ$ can be built as the distribution of preimages of a generic point and that the expansive periodic points are equidistributed on the support of $μ$. Using this results, we will give a characterization of infinite unique sets for polynomials.