Reduction of superintegrable systems: the anisotropic harmonic oscillator
arXiv:0807.1047 · doi:10.1103/PhysRevE.78.046608
Abstract
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.
6 pages. Version accepted in Physical Review E