{
  "id": "2205.06156",
  "version": "v1",
  "published": "2022-05-12T15:26:56.000Z",
  "updated": "2022-05-12T15:26:56.000Z",
  "title": "No Periodic Geodesics in $J^k(\\mathbb{R},\\mathbb{R}^n)$",
  "authors": [
    "Alejandro Bravo-Doddoli"
  ],
  "categories": [
    "math.DS",
    "math.DG"
  ],
  "abstract": "The space of $k$-jets of $n$ real function of one real variable $x$ admits the structure of a Carnot group, which then has an associated Hamiltonian geodesic flow. As in any Hamiltonian flow, a natural question is the existence of periodic solutions. Does the space of $k$-jets have periodic geodesics? This study will demonstrate the integrability of \\sR geodesic flow, characterize and classify the \\sR geodesics in the space of $k$-jets, and show that they are never periodic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-12T15:26:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic geodesics",
      "associated hamiltonian geodesic flow",
      "carnot group",
      "real function",
      "periodic solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}