2004/07/27 by Charles Favre, Juan Rivera-Letelier, Favre, Charles +2
Mathematics · Psychology · #11S80 #37F10 #Dynamical Systems (math.DS) #FOS: Mathematics #Mental Health Research Topics #Number Theory (math.NT) #advanced mathematical theories #math.DS #math.NT #msc:11S80 #msc:37F10
paper · pdf · doi:10.48550/arxiv.math/0407469
7 pages, accepted in the Comptes Rendus de l'Academie des Sciences
arxiv created 2004/07/27 · openalex publication_date 2004/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove an analog of the famous equidistribution theorem of Brolin for rational mappings in one variable defined over the p-adic field Cp. 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 Cp. 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.