Brolin's equidistribution theorem in p-adic dynamics

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 P¹ (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).