{
  "id": "2405.17783",
  "version": "v1",
  "published": "2024-05-28T03:26:46.000Z",
  "updated": "2024-05-28T03:26:46.000Z",
  "title": "Hyperbolic motions in the $N$-body problem with homogeneous potentials",
  "authors": [
    "Guowei Yu"
  ],
  "comment": "Accepted by DCDS-A with minor revision",
  "categories": [
    "math.DS"
  ],
  "abstract": "In the $N$-body problem, a motion is called hyperbolic, when the mutual distances between the bodies go to infinity with non-zero limiting velocities as time goes to infinity. For Newtonian potential, in \\cite{MV20} Maderna and Venturelli proved that starting from any initial position there is a hyperbolic motion with any prescribed limiting velocities at infinity. Recently based on a different approach, Liu, Yan and Zhou \\cite{LYZ21} generalized this result to a larger class of $N$-body problem. As the proof in \\cite{LYZ21} is quite long and technical, we give a simplified proof for homogeneous potentials following the approach given in the latter paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-28T03:26:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37N05",
      "70F10",
      "70F15"
    ],
    "keywords": [
      "body problem",
      "hyperbolic motion",
      "homogeneous potentials",
      "newtonian potential",
      "non-zero limiting velocities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}