{
  "id": "1711.05077",
  "version": "v1",
  "published": "2017-11-14T12:22:24.000Z",
  "updated": "2017-11-14T12:22:24.000Z",
  "title": "Application of Morse index in weak force $N$-body problem",
  "authors": [
    "Guowei Yu"
  ],
  "comment": "17 pages. Please let me know, if you have any comments!",
  "categories": [
    "math.DS"
  ],
  "abstract": "Due to collision singularities, the Lagrange action functional of the N-body problem in general is only lower semi-continuous in the space of Sobolev paths. Because of this, the usual critical point theory can not be applied to this problem directly. We introduce a notation called weak critical point for such an action functional, as a generalization of the usual critical point. A corresponding definition of Morse index for such a weak critical point will also be defined. Moreover it will be shown that the Morse index gives an upper bound of the number of possible binary collisions in a weak critical point of the $N$-body problem with weak force potentials including the Newtonian potential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-14T12:22:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70F07",
      "37N05"
    ],
    "keywords": [
      "morse index",
      "weak critical point",
      "application",
      "weak force potentials",
      "usual critical point theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}