{
  "id": "1807.10527",
  "version": "v1",
  "published": "2018-07-27T10:41:40.000Z",
  "updated": "2018-07-27T10:41:40.000Z",
  "title": "Spectrum of the second variation",
  "authors": [
    "Andrei Agrachev"
  ],
  "comment": "22 pages",
  "categories": [
    "math.OC",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Second variation of a smooth optimal control problem at a regular extremal is a symmetric Fredholm operator. We study asymptotics of the spectrum of this operator and give an explicit expression for its determinant in terms of solutions of the Jacobi equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-27T10:41:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "second variation",
      "smooth optimal control problem",
      "symmetric fredholm operator",
      "jacobi equation",
      "study asymptotics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}