Theoreme d'equidistribution de Brolin en dynamique p-adique

Abstract

We prove an analog of the famous equidistribution theorem of Brolin for rational mappings in one variable defined over the p-adic field C_p. We construct a mixing invariant probability measure which describes the asymptotic distribution of iterated preimages of a given point. This measure is supported on the Berkovich space associated to the projective line over C_p. We show that its support is precisely the Julia set as defined by Rivera-Letelier. Our results are based on the construction of a Laplace operator on real trees with arbitrary number of branching as done by Favre-Jonsson.