Integrable generalizations of oscillator and Coulomb systems via   action-angle variables
  Oscillator and Coulomb systems on N-dimensional spaces of constant curvature can be generalized by replacing their angular degrees of freedom with a compact integrable (N-1)-dimensional system. We present the action-angle formulation of such models in terms of theradial degree of freedom and the action-angle variables of the angular subsystem. As an example, we construct the spherical and pseudospherical generalization of the two-dimensional superintegrable models introduced by Tremblay, Turbiner and Winternitz and by Post and Winternitz. We demonstrate the superintegrability of these systems and give their hidden constant of motion. 
Tigran Hakobyan, Olaf Lechtenfeld, Armen Nersessian, Armen   Saghatelian, Vahagn Yeghikyan
hep-th math-ph math.MP