Théorème d'équidistribution 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 P 1 ( C p ) associated to P 1 ( C p ) . We show that its support is precisely the Julia set of R 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 in (C. Favre, M. Jonsson, The valuative tree, Lecture Notes in Math., Springer-Verlag, in press). To cite this article: C. Favre, J. Rivera-Letelier, C. R. Acad. Sci. Paris, Ser. I 339 (2004).