Equidistribution of repelling periodic points in non-archimedean dynamics

Non-archimedean dynamics is the study of the limiting behaviour of points, measures and subsets under the iteration of an endomorphism of a non archimedean analytic space. The most studied case is the iteration of rational functions (and in particular polynomials) mapping the projective line onto itself. I will explain the basics of this type of study and talk about some work I have done on the question posed by Favre and Rivera-Letelier on whether periodic repelling points equidistribute to the canonical measure, which is well known to happen in the complex case. We will see that at least in the case of polynomials we can answer positively.