{
  "id": "1507.02892",
  "version": "v1",
  "published": "2015-07-10T13:27:36.000Z",
  "updated": "2015-07-10T13:27:36.000Z",
  "title": "Shape Space Figure $8$ Solutions of three body problem with two equal masses",
  "authors": [
    "Guowei Yu"
  ],
  "comment": "29 pages, 4 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "In an unpublished paper by Richard Montgomery, the author claimed to prove the existence of shape space Figure-$8$ solutions of the Newtonian three body problem with two equal masses (they look like a figure $8$'s in the shape space, that is different from the famous Figure-$8$ solution proved by Chenciner and Montgomery). However there is an error in the proof and the problem is still open. In this paper, based on a new local deformation result, we prove the existence of such solutions in weak force potential, $1<\\alpha <2$ and in Newtonian potential under an extra condition. This result can be seen as a small step in the program of realizing (reduced) syzygy sequences in the three body problem that were proposed by Montgomery.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-10T13:27:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70F07",
      "37N05"
    ],
    "keywords": [
      "body problem",
      "shape space figure",
      "equal masses",
      "local deformation result",
      "weak force potential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150702892Y"
    }
  }
}