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

TL;DR

This paper constructs an equilibrium measure for polynomial correspondences, showing it as the distribution of preimages of generic points and demonstrating equidistribution of periodic points, with applications to characterizing infinite unique sets for polynomials.

Contribution

It introduces a method to build an equilibrium measure for polynomial correspondences and links it to preimages and periodic points, providing new insights into polynomial dynamics.

Findings

Equilibrium measure constructed for polynomial correspondences.

Periodic points are equidistributed on the measure's support.

Characterization of infinite unique sets for polynomials achieved.

Abstract

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