Complete integrability of geodesics in toric Sasaki-Einstein space T 1,1 and action-angle variables

Abstract

Radiation emitted by a charged particle undergoing Brownian motion in a magnetic field AIP Conference Proceedings 1796, 020004 (2017) Abstract. We describe the construction of the integrals of geodesic motions in the homogeneous Sasaki-Einstein space T 1,1 . For this purpose we use the knowledge of the complete set of Killing vectors and Killing tensors of this space. We discuss the integrability of geodesics and construct explicitly the action-angle variables. We find that two pairs of frequencies of the geodesic motions are resonant giving way to chaotic behavior when the integrable Hamiltonian is perturbed by a small nonintegrable piece.