
Symmetry in Nonlinear Mathematical Physics  2009
Francisco Jose Herranz (Universidad de Burgos, Spain)
Symmetries and superintegrability of new Ndimensional nonlinear oscillators from Euclidean systems
Abstract:
We start with the classical harmonic oscillator and KeplerCoulomb systems on the Ndimensional Euclidean space. By applying the Stackel transform (or couplingconstant metamorphosis) we obtain two families of maximally superintegrable Ndimensional systems; each of them is parametrized by two free real parameters. Furthermore, in spite of the harmonic oscillator or Kepler origin, all the resulting potentials are interpreted as ''intrinsic'' oscillators on spherical symmetric spaces of nonconstant curvature (which are of a nonlinear nature). The resulting set of (2N–2) functionally independent constants of the motion are also explicitly presented. As a byproduct, the TaubNUT system is recovered as a particular case of the family of nonlinear oscillators coming from the Euclidean Kepler–Coulomb system. Finally, the nonlinear potentials are briefly analysed with respect to the harmonic oscillator one.

