{
  "id": "1502.06278",
  "version": "v1",
  "published": "2015-02-22T22:29:45.000Z",
  "updated": "2015-02-22T22:29:45.000Z",
  "title": "Globally minimizing parabolic motions in the Newtonian N-body problem",
  "authors": [
    "Ezequiel Maderna",
    "Andrea Venturelli"
  ],
  "comment": "26 pages, 2 figures",
  "journal": "Archive for Rational Mechanics and Analysis, October 2009, volume 194, issue 1, pp 283-313",
  "doi": "10.1007/s00205-008-0175-8",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the $N$-body problem in $\\mathbb{R}^d$ with the newtonian potential $1/r$. We prove that for every initial configuration $x_i$ and for every minimizing normalized central configuration $x_0$, there exists a collision-free parabolic solution starting from $x_i$ and asymptotic to $x_0$. This solution is a minimizer in every time interval. The proof exploits the variational structure of the problem, and it consists in finding a convergent subsequence in a family of minimizing trajectories. The hardest part is to show that this solution is parabolic and asymptotic to $x_0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-22T22:29:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70F10"
    ],
    "keywords": [
      "globally minimizing parabolic motions",
      "newtonian n-body problem",
      "collision-free parabolic solution",
      "newtonian potential",
      "convergent subsequence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}