Absence of mixing for interval translation mappings and some generalizations

Abstract: We consider piecewise monotone maps, we show that an ergodic measure for which the map is invertible almost everywhere can not be mixing. It follows that every ergodic measure for an interval translation mapping is not mixing. We also show that double rotations without periodic points have an ergodic but not weakly mixing invariant measure. This article is dedicated to the memory of Anatoly Mikhailovich Stepin.