{
  "id": "2205.00960",
  "version": "v1",
  "published": "2022-05-02T15:01:59.000Z",
  "updated": "2022-05-02T15:01:59.000Z",
  "title": "On the solution manifold of a differential equation with a delay which has a zero",
  "authors": [
    "Hans-Otto Walther"
  ],
  "comment": "11 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "For a differential equation with a state-dependent delay we show that the associated solution manifold $X_f$ of codimnsion 1 in the space $C^1([-r,0],\\mathbb {R})$ is an almost graph over a hyperplane, which implies that $X_f$ is diffeomorphic to the hyperplane. For the case considered previous results only provide a covering by 2 almost graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-02T15:01:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K43"
    ],
    "keywords": [
      "differential equation",
      "state-dependent delay",
      "associated solution manifold",
      "hyperplane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}