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

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.

12 pages, to appear in Prog. Theor. Exp. Phys

References in corpus (2)

• Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}
• Symmetries and Integrability