Decay of correlations and mixing properties in a dynamical system with zero K–S entropy

Abstract

We consider the ergodic skew product of translations on the torus ${\Bbb T}^{2}$. We characterize a class of smooth functions with exponential correlation decay rate and a class of subsets with an exponential rate of mixing. We show that the class of functions with sub-exponential correlation decay rate is generic. We also characterize another class of subsets with mixing rate of the order of $1/t$.