Superintegrability of (generalized) Calogero models with oscillator or   Coulomb potential
  We deform N-dimensional (Euclidean, spherical and hyperbolic) oscillator and Coulomb systems, replacing their angular degrees of freedom by those of a generalized rational Calogero model. Using the action-angle description, it is established that maximal superintegrability is retained. For the rational Calogero model with Coulomb potential, we present all constants of motion via matrix model reduction. In particular, we construct the analog of the Runge-Lenz vector. 
Tigran Hakobyan, Olaf Lechtenfeld, Armen Nersessian
hep-th math-ph math.MP