Keplerian shear in ergodic theory

TL;DR

This paper explores Keplerian shear within ergodic theory, providing criteria for its occurrence, analyzing its typicality and speed, and discussing both Hamiltonian and non-Hamiltonian examples.

Contribution

It introduces a sufficient condition for Keplerian shear in dynamical systems and examines its prevalence and rate of mixing in various contexts.

Findings

Established a criterion for Keplerian shear to occur.

Analyzed the genericity of Keplerian shear in systems.

Discussed the speed of mixing in specific cases.

Abstract

Many integrable physical systems exhibit Keplerian shear. We look at this phenomenon from the point of view of ergodic theory, where it can be seen as mixing conditionally to an invariant $\sigma$-algebra. In this context, we give a sufficient criterion for Keplerian shear to appear in a system, investigate its genericity and, in a few cases, its speed. Some additional, non-Hamiltonian, examples are discussed.