Keplerian shear with Rajchman property

Abstract

The Keplerian shear was introduced within the context of measure preserving dynamical systems by Damien Thomine, as a version of mixing for non ergodic systems. In this study we provide a characterization of the Keplerian shear using Rajchman measure, for some flows on tori bundles. Our work applies to dynamical systems with singularities or with non-absolutely continuous measures. We relate the speed of decay of conditional correlations with the Rajchman order of the measures. Some of these results are extended to the case of compact Lie group bundles.