{
  "id": "1311.6061",
  "version": "v1",
  "published": "2013-11-23T22:12:00.000Z",
  "updated": "2013-11-23T22:12:00.000Z",
  "title": "Periodic Orbits in the Kepler-Heisenberg Problem",
  "authors": [
    "Corey Shanbrom"
  ],
  "comment": "19 pages, 3 figures",
  "categories": [
    "math.DS",
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "One can formulate the classical Kepler problem on the Heisenberg group, the simplest sub-Riemannian manifold. We take the sub-Riemannian Hamiltonian as our kinetic energy, and our potential is the fundamental solution to the Heisenberg sub-Laplacian. The resulting dynamical system is known to contain a fundamental integrable subsystem. Here we use variational methods to prove that the Kepler-Heisenberg system admits periodic orbits with $k$-fold rotational symmetry for any odd integer $k\\geq 3$. Approximations are shown for $k=3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-23T22:12:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C17",
      "37N05",
      "37J45",
      "70H12",
      "70H06"
    ],
    "keywords": [
      "kepler-heisenberg problem",
      "kepler-heisenberg system admits periodic orbits",
      "simplest sub-riemannian manifold",
      "fold rotational symmetry",
      "heisenberg group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.6061S"
    }
  }
}