{
  "id": "2007.01741",
  "version": "v1",
  "published": "2020-07-03T15:00:45.000Z",
  "updated": "2020-07-03T15:00:45.000Z",
  "title": "Fixed points and the inverse problem for central configurations",
  "authors": [
    "D. L. Ferrario"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Central configurations play an important role in the dynamics of the $n$-body problem: they occur as relative equilibria and as asymptotic configurations in colliding trajectories. We illustrate how they can be found as projective fixed points of self-maps defined on the shape space, and some results on the inverse problem in dimension $1$, i.e. finding (positive or real) masses which make a given collinear configuration central. This survey article introduces readers to the recent results of the author, also unpublished, showing an application of the fixed point theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-03T15:00:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse problem",
      "central configurations play",
      "collinear configuration central",
      "important role",
      "body problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}