2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61922We use Ratner's theorem to compute the asymptotics of the number of (cylinders of) periodic trajectories in a rectangle with a barrier, assuming that the location p/q of the barrier is rational. We also show that as q tends to infinity, the constant in the asymptotic formula tends to the constant for the generic genus 2 flat surface.Dynamical SystemsMathematical Physics37A99 (primary) 37E15, 37D40, 37D50 (secondary)text