Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the St

  title={Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the St},
  author={{\'A}ngel Ballesteros and Alberto Enciso and Francisco J. Herranz and Orlando Ragnisco and Danilo Riglioni},
The Stackel transform is applied to the geodesic motion on Euclidean space, through the harmonic oscillator and Kepler{Coloumb potentials, in order to obtain ma- ximally superintegrable classical systems on N-dimensional Riemannian spaces of noncon- stant curvature. By one hand, the harmonic oscillator potential leads to two families of superintegrable systems which are interpreted as an intrinsic Kepler{Coloumb system on a hyperbolic curved space and as the so-called Darboux III oscillator. On… 

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