Action-angle variables for geodesic motions in Sasaki-Einstein spaces $Y^{p,q}$

TL;DR

This paper employs action-angle variables to analyze geodesic motions in 5D Sasaki-Einstein spaces, revealing integrability and potential chaos under perturbations.

Contribution

It introduces a novel application of action-angle variables to study geodesics in $Y^{p,q}$ spaces, highlighting integrability and chaos indicators.

Findings

Hamiltonian involves fewer action variables

One fundamental frequency is zero

System shows potential chaos when perturbed

Abstract

We use the action-angle variables to describe the geodesic motions in the $5$-dimensional Sasaki-Einstein spaces $Y^{p,q}$. This formulation allows us to study thoroughly the complete integrability of the system. We find that the Hamiltonian involves a reduced number of action variables. Therefore one of the fundamental frequency is zero indicating a chaotic behavior when the system is perturbed.