{
  "id": "2102.12741",
  "version": "v1",
  "published": "2021-02-25T09:10:51.000Z",
  "updated": "2021-02-25T09:10:51.000Z",
  "title": "Spiraling of sub-Riemannian geodesics around the Reeb flow in the 3D contact case",
  "authors": [
    "Yves Colin de Verdière",
    "Luc Hillairet",
    "Emmanuel Trélat"
  ],
  "categories": [
    "math.DG",
    "math.MG",
    "math.SG"
  ],
  "abstract": "We consider a closed three-dimensional contact sub-Riemannian manifold. The objective of this note is to provide a precise description of the sub-Riemannian geodesics with large initial momenta: we prove that they \"spiral around the Reeb orbits\", not only in the phase space but also in the configuration space. Our analysis is based on a normal form along any Reeb orbit due to Melrose.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-25T09:10:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "3d contact case",
      "sub-riemannian geodesics",
      "reeb flow",
      "closed three-dimensional contact sub-riemannian manifold",
      "reeb orbit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}