{
  "id": "2211.03619",
  "version": "v1",
  "published": "2022-11-07T15:11:16.000Z",
  "updated": "2022-11-07T15:11:16.000Z",
  "title": "Singularities of 3d vector fields preserving the form of Martinet",
  "authors": [
    "Stavros Anastassiou"
  ],
  "comment": "11 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the local structure of vector fields on $\\mathbb{R}^3$ which preserve the Martinet $1$-form $\\alpha=(1+x)dy\\pm zdz$. We present the classification of their singularities, up to diffeomorphisms preserving the form $\\alpha$, as well as their transversal unfoldings. We are thus able to provide a fairly complete list of the bifurcations such vector fields undergo.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-07T15:11:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C15",
      "37J10",
      "58K45",
      "53D10"
    ],
    "keywords": [
      "3d vector fields preserving",
      "singularities",
      "vector fields undergo",
      "transversal unfoldings",
      "fairly complete list"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}