{
  "id": "1504.06228",
  "version": "v1",
  "published": "2015-04-23T15:41:09.000Z",
  "updated": "2015-04-23T15:41:09.000Z",
  "title": "Harmonic Oscillator on the $SO(2,2)$ hyperboloid",
  "authors": [
    "D. R. Petrosyan",
    "G. S. Pogosyan"
  ],
  "comment": "17 pages, 9 figures, PDFLaTex",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In the present work the problem of the motion of the classical particle in the field of harmonic oscillator in the hyperbolic space $H_2^2: \\, z_0^2+z_1^2-z_2^2-z_3^2=R^2$ has been solved. We have shown that all the finite classical trajectories are closed and periodic. The orbits of motion are ellipses or circles for bounded motion and parabolas and hyperbolas for infinite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-23T15:41:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70H20",
      "35F21"
    ],
    "keywords": [
      "harmonic oscillator",
      "hyperboloid",
      "hyperbolic space",
      "finite classical trajectories",
      "classical particle"
    ],
    "note": {
      "typesetting": "PDFLaTeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150406228P"
    }
  }
}