2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69630We study the lower and upper local rates of Poincare recurrence of rotations on the circle by means of symbolic dynamics. As a consequence, we show that if the lower rate of Poincare recurrence of an ergodic dynamical system (X,F,mu,T) is greater or equal to 1 mu-almost everywhere, then it is weakly mixing.To appear in Discrete and Continuous Dynam. Syst. (Series A)Dynamical Systemstext