Theoreme d'equidistribution de Brolin en dynamique p-adique

Details Theoreme d'equidistribution de Brolin en dynamique p-adique Theoreme d'equidistribution de Brolin en dynamique p-adique

2004-07-27

arxiv.org/abs/math/0407469v1

Mathematics

Dynamical Systems

7 pages, accepted in the Comptes Rendus de l'Academie des Sciences

Scientific paper

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.

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