Keplerian shear with Rajchman property

TL;DR

This paper characterizes Keplerian shear in measure-preserving dynamical systems using Rajchman measures, linking decay of correlations to measure properties, and extends results to systems with singularities and Lie group bundles.

Contribution

It introduces a novel characterization of Keplerian shear via Rajchman measures, applicable to systems with singularities and non-absolutely continuous measures.

Findings

Decay speed of correlations relates to Rajchman order.

Characterization of Keplerian shear for flows on tori bundles.

Extension of results to compact Lie group bundles.

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.