https://doi.org/10.1140/epjc/s10052-016-4348-6
Regular Article - Theoretical Physics
Integrability of geodesics and action-angle variables in Sasaki–Einstein space 
Department Theoretical Physics, National Institute of Physics and Nuclear Engineering, Magurele, Bucharest, Romania
* e-mail: mvisin@theory.nipne.ro
Received:
14
April
2016
Accepted:
2
September
2016
Published online:
13
September
2016
We briefly describe the construction of Stäkel–Killing and Killing–Yano tensors on toric Sasaki–Einstein manifolds without working out intricate generalized Killing equations. The integrals of geodesic motions are expressed in terms of Killing vectors and Killing–Yano tensors of the homogeneous Sasaki–Einstein space . We discuss the integrability of geodesics and construct explicitly the action-angle variables. Two pairs of frequencies of the geodesic motions are resonant giving way to chaotic behavior when the system is perturbed.
© The Author(s), 2016
