{
  "id": "1501.01258",
  "version": "v1",
  "published": "2015-01-06T18:42:39.000Z",
  "updated": "2015-01-06T18:42:39.000Z",
  "title": "Superintegrability of the Post-Winternitz system on spherical and hyperbolic spaces",
  "authors": [
    "Manuel F. Ranada"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1403.6266",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The properties of the Tremblay-Turbiner-Winternitz system (related to the harmonic oscillator) were recently studied on the two-dimensional spherical $S_{\\kappa}^2$ ($\\kappa>0$) and hiperbolic $H_{\\kappa}^2$ ($\\kappa<0$) spaces. In particular, it was proved the higher-order superintegrability of the TTW system by making use of (i) a curvature-dependent formalism, and (ii) existence of a complex factorization for the additional constant of motion. Now a similar study is presented for the Post-Winternitz system (related to the Kepler problem). The curvature $\\kappa$ is considered as a parameter and all the results are formulated in explicit dependence of $\\kappa$. This technique leads to a correct definition of the Post-Winternitz (PW) system on spaces with curvature $\\kappa$, to a proof of the existence of higher-order superintegrability (in both cases, $\\kappa>0$ and $\\kappa<0$), and to the explicit expression of the constants of motion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-06T18:42:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J35",
      "70H06"
    ],
    "keywords": [
      "post-winternitz system",
      "hyperbolic spaces",
      "higher-order superintegrability",
      "explicit expression",
      "ttw system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}