{
  "id": "1505.05246",
  "version": "v1",
  "published": "2015-05-20T05:21:51.000Z",
  "updated": "2015-05-20T05:21:51.000Z",
  "title": "Linear stability of the n-gon relative equilibria of the (1+n)-body problem",
  "authors": [
    "Xingbo Xu"
  ],
  "comment": "published in 2013",
  "doi": "10.1007/s12346-012-0089-6",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the linear stabilities of the regular n-gon relative equilibria of the (1+n)-body problem. It is shown that there exist at most two kinds of infinitesimal bodies arranged alternatively at the vertices of a regular n-gon when n is even, and only one set of identical infinitesimal bodies when n is odd. In the case of n even, the regular n-gon relative equilibrium is shown to be linearly stable when n>=14. In each case of n=8,10,12, linear stability can also be preserved if the ratio of two kinds of masses belongs to an open interval. When n is odd, the related conclusion on the linear stability is recalled.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-20T05:21:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear stability",
      "regular n-gon relative equilibrium",
      "identical infinitesimal bodies",
      "masses belongs",
      "open interval"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150505246X"
    }
  }
}