École polytechnique – Centre de Mathématiques Laurent Schwartz

9h30 – Groupe de Travail autour de l'article "The joint spectrum" de Breuillard et Ser

14h00 – Yüsuke Okuyama (Kyoto Institute of Technology)

"Equidistribution in non-archimedean dynamics under no potentially good reductions"

Abstract: Let K be an algebraically closed field that is complete with respect to a non-trivial and non-archimedean absolute value, and f be a rational function on the projective line defined over K and of degree d>1. In this talk, we focus on the weak convergence of the sequence ([fⁿ=g]/(dⁿ+deg(g)))_n of the effective divisors (or purely atomic measures) defined by the roots of the equation fⁿ=g (for the n-th iterates fⁿ of f and a non-constant rational function g) towards the canonical measure of f on the Berkovich projective line over K. This convergence has been known by Favre--Rivera-Letelier if K is of characteristic 0, and we will establish it under the assumption that f has no potentially good reductions (and K is of any characteristic).