Action-angle approach to the geodesic motions in the homogeneous Sasaki-Einstein space T 1,1

Abstract

The complete integrability of geodesics in the homogeneous Sasaki-Einstein space T1,1 makes possible the explicit construction of the action-angle variables. This parametrization of the phase space represents a useful tool for developing perturbation theory. We find that two pairs of fundamental frequencies of the geodesic motions are resonant indicating a chaotic behavior when the integrable Hamiltonian is perturbed by a small non-integrable piece.