{
  "id": "2110.12806",
  "version": "v4",
  "published": "2021-10-25T11:06:28.000Z",
  "updated": "2022-04-08T19:37:25.000Z",
  "title": "A Necessary and Sufficient Condition for a Self-Diffeomorphism of a Smooth Manifold to be the Time-1 Map of the Flow of a Differential Equation",
  "authors": [
    "Jeffrey J. Rolland"
  ],
  "comment": "This paper may be a little \"light\" on content and therefore not publishable; however, it doesn't hurt (I don't think) to upload it to the arXiv for comments. Having said that, I would greatly appreciate and and all comments on the paper",
  "categories": [
    "math.DS"
  ],
  "abstract": "In topological dynamics, one considers a topological space $X$ and a self-map $f: X \\to X$ of $X$ and studies the self-map's properties. In global analysis, one considers a smooth manifold $M^n$ and a differential equation $\\xi: M \\to TM$ on $M$ and studies the flow $\\Phi_t: M \\times \\mathbb{R} \\to M$ of the differential equation. In this paper, we consider a necessary and sufficient condition for a self-diffeomorphism $f$ of a manifold $M$ to be the time-1 map $\\Phi_1$ of the flow of a differential equation on $M$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2022-04-08T19:37:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C10",
      "37C05",
      "58-01"
    ],
    "keywords": [
      "differential equation",
      "sufficient condition",
      "smooth manifold",
      "self-diffeomorphism",
      "self-maps properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}