{
  "id": "1403.6266",
  "version": "v1",
  "published": "2014-03-25T09:24:34.000Z",
  "updated": "2014-03-25T09:24:34.000Z",
  "title": "The Tremblay-Turbiner-Winternitz system on spherical and hyperbolic spaces : Superintegrability, curvature-dependent formalism and complex factorization",
  "authors": [
    "Manuel F. Ranada"
  ],
  "comment": "one figure",
  "journal": "J. Phys. A (Math. Theor.) 47, no. 16, 165203 (2014)",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The higher-order superintegrability of the Tremblay-Turbiner-Winternitz system (related to the harmonic oscillator) is studied on the two-dimensional spherical and hiperbolic spaces, $S_\\k^2$ ($\\k>0$), and $H_{\\k}^2$ ($\\k<0$). The curvature $\\kappa$ is considered as a parameter and all the results are formulated in explicit dependence of $\\kappa$. The idea is that the additional constant of motion can be factorized as the product of powers of two particular rather simple complex functions (here denoted by $M_r$ and $N_\\phi$). This technique leads to a proof of the superintegrability of the Tremblay-Turbiner-Winternitz system on $S_\\k^2$ ($\\k>0$) and $H_{\\k}^2$ ($\\k<0$), and to the explicit expression of the constants of motion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-25T09:24:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J35",
      "70H06"
    ],
    "keywords": [
      "tremblay-turbiner-winternitz system",
      "curvature-dependent formalism",
      "hyperbolic spaces",
      "complex factorization",
      "superintegrability"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/47/16/165203",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2014,
      "month": "Apr",
      "volume": 47,
      "number": 16,
      "pages": 165203
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1301163,
      "adsabs": "2014JPhA...47p5203R"
    }
  }
}