An a priori bound of rational functions on the Berkovich projective line

2018/05/19 by Yûsuke Okuyama, Okuyama, Yûsuke
Mathematics · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1805.07668

openalex publication_date 2018/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a locally uniform a priori bound on the dynamics of a rational function f of degree >1 on the Berkovich projective line over an algebraically closed field of any characteristic that is complete with respect to a non-trivial and non-archimedean absolute value, and deduce an equidistribution result for moving targets towards the equilibrium (or canonical) measure μ_f, under the no potentially good reductions condition. This partly answers a question posed by Favre and Rivera-Letelier.

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