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Integrability of geodesics and action-angle variables in Sasaki-Einstein space $T^{1,1}$

We briefly describe the construction of Stä\-kel-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 Kill\-ing-Yano tensors of the homogeneous Sasaki-Einstein space $T^{1,1}$. 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.