{
  "id": "1509.00419",
  "version": "v1",
  "published": "2015-09-01T17:59:17.000Z",
  "updated": "2015-09-01T17:59:17.000Z",
  "title": "Hamilton-Jacobi theory, Symmetries and Coisotropic Reduction",
  "authors": [
    "Manuel de León",
    "David Martín de Diego",
    "Miguel Vaquero"
  ],
  "comment": "30 pages",
  "categories": [
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "Reduction theory has played a major role in the study of Hamiltonian systems. On the other hand, the Hamilton-Jacobi theory is one of the main tools to integrate the dynamics of certain Hamiltonian problems and a topic of research on its own. Moreover, the construction of several symplectic integrators rely on approximations of a complete solution of the Hamilton-Jacobi equation. The natural question that we address in this paper is how these two topics (reduction and Hamilton-Jacobi theory) fit together. We obtain a reduction and reconstruction procedure for the Hamilton-Jacobi equation with symmetries, even in a generalized sense to be clarified below. Several applications and relations to other reductions of the Hamilton-Jacobi theory are shown in the last section of the paper. It is remarkable that as a by-product we obtain a generalization of the Ge-Marsden reduction procedure. Quite surprinsingly, the classical ansatzs available in the literature to solve the Hamilton-Jacobi equation are also particular instances of our framework.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-01T17:59:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamilton-jacobi theory",
      "coisotropic reduction",
      "hamilton-jacobi equation",
      "symmetries",
      "ge-marsden reduction procedure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}