Reduction of superintegrable systems: the anisotropic harmonic   oscillator
  We introduce a new 2N--parametric family of maximally superintegrable systems in N dimensions, obtained as a reduction of an anisotropic harmonic oscillator in a 2N--dimensional configuration space. These systems possess closed bounded orbits and integrals of motion which are polynomial in the momenta. They generalize known examples of superintegrable models in the Euclidean plane. 
Miguel A. Rodriguez, Piergiulio Tempesta, Pavel Winternitz