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Local rates of Poincare recurrence for rotations and weak mixing

JR Chazottes·F. Durand
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Abstract

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.

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JR Chazottes, F. Durand. 2003-12-17. Local rates of Poincare recurrence for rotations and weak mixing. https://arxiv.org/abs/math/0312328

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