{
  "id": "0710.0843",
  "version": "v2",
  "published": "2007-10-03T17:24:06.000Z",
  "updated": "2008-05-14T10:16:37.000Z",
  "title": "Superintegrable anharmonic oscillators on N-dimensional curved spaces",
  "authors": [
    "Angel Ballesteros",
    "Alberto Encisco",
    "Francisco J. Herranz",
    "Orlando Ragnisco"
  ],
  "comment": "10 pages. Based on the contribution presented at the \"17th Conference on Nonlinear Evolution Equations and Dynamical Systems\" NEEDS 2007. L'Ametlla de Mar, Spain, June 17-24, 2007. Minor changes and two references added. To appear in J. Nonlinear Math. Phys",
  "journal": "J. Nonlinear Math. Phys. 15 suppl. 3 (2008) 43-52",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "The maximal superintegrability of the intrinsic harmonic oscillator potential on N-dimensional spaces with constant curvature is revisited from the point of view of sl(2)-Poisson coalgebra symmetry. It is shown how this algebraic approach leads to a straightforward definition of a new large family of quasi-maximally superintegrable perturbations of the intrinsic oscillator on such spaces. Moreover, the generalization of this construction to those N-dimensional spaces with non-constant curvature that are endowed with sl(2)-coalgebra symmetry is presented. As the first examples of the latter class of systems, both the oscillator potential on an N-dimensional Darboux space as well as several families of its quasi-maximally superintegrable anharmonic perturbations are explicitly constructed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-05-14T10:16:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "n-dimensional curved spaces",
      "superintegrable anharmonic oscillators",
      "n-dimensional spaces",
      "intrinsic harmonic oscillator potential",
      "n-dimensional darboux space"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "publication": {
      "doi": "10.2991/jnmp.2008.15.s3.5",
      "journal": "Journal of Nonlinear Mathematical Physics",
      "year": 2008,
      "volume": 15,
      "pages": 43
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JNMP...15S..43B"
    }
  }
}