Local rates of Poincare recurrence for rotations and weak mixing
We 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.
math.DS↗