{
  "id": "1304.3377",
  "version": "v1",
  "published": "2013-04-11T17:23:11.000Z",
  "updated": "2013-04-11T17:23:11.000Z",
  "title": "On Hamiltonian flows whose orbits are straight lines",
  "authors": [
    "Hans Koch",
    "Héctor E. Lomelí"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider real analytic Hamiltonians whose flow depends linearly on time. Trivial examples are Hamiltonians $H(q,p)$ that do not depend on the coordinate $q$. By a theorem of Moser, every polynomial Hamiltonian of degree 3 reduces to such a $q$-independent Hamiltonian via a linear symplectic change of variables. We show that such a reduction is impossible, in general, for polynomials of degree 4 or higher. But we give a condition that implies linear-symplectic conjugacy to another simple class of Hamiltonians. The condition is shown to hold for all nondegenerate Hamiltonians that are homogeneous of degree 4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-11T17:23:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26C05",
      "37J10",
      "37M15",
      "14E07",
      "58C25"
    ],
    "keywords": [
      "hamiltonian flows",
      "straight lines",
      "implies linear-symplectic conjugacy",
      "linear symplectic change",
      "real analytic hamiltonians"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.3377K"
    }
  }
}