{
  "id": "math-ph/0610040",
  "version": "v1",
  "published": "2006-10-17T21:10:25.000Z",
  "updated": "2006-10-17T21:10:25.000Z",
  "title": "Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature",
  "authors": [
    "Angel Ballesteros",
    "Francisco J. Herranz"
  ],
  "comment": "12 pages",
  "journal": "J.Phys.A40:F51-F60,2007",
  "doi": "10.1088/1751-8113/40/2/F01",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "An infinite family of classical superintegrable Hamiltonians defined on the N-dimensional spherical, Euclidean and hyperbolic spaces are shown to have a common set of (2N-3) functionally independent constants of the motion. Among them, two different subsets of N integrals in involution (including the Hamiltonian) can always be explicitly identified. As particular cases, we recover in a straightforward way most of the superintegrability properties of the Smorodinsky-Winternitz and generalized Kepler-Coulomb systems on spaces of constant curvature and we introduce as well new classes of (quasi-maximally) superintegrable potentials on these spaces. Results here presented are a consequence of the sl(2) Poisson coalgebra symmetry of all the Hamiltonians, together with an appropriate use of the phase spaces associated to Poincare and Beltrami coordinates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-17T21:10:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J35",
      "22Exx",
      "02.40.Ky",
      "02.30.Ik"
    ],
    "keywords": [
      "constant curvature",
      "n-dimensional spaces",
      "universal integrals",
      "superintegrable systems",
      "hamiltonian"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 730321
    }
  }
}