{
  "id": "2309.14579",
  "version": "v1",
  "published": "2023-09-25T23:52:55.000Z",
  "updated": "2023-09-25T23:52:55.000Z",
  "title": "Critical points at infinity of the 3-body Problem in $\\mathbb{R}^4$",
  "authors": [
    "Alain Albouy",
    "Holger R. Dullin"
  ],
  "comment": "6 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that critical points at infinity in the 3-body problem in $\\mathbb{R}^4$ do not realize the infimum of the energy. This completes our previous work [Journal of Geometric Mechanics, 12, pp323-341 (2020), doi:10.3934/jgm.2020012] on the existence of Lyapunov stable relative periodic orbits in the 3-body problem in $\\mathbb{R}^4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-25T23:52:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37N05",
      "70F10",
      "70F15",
      "70H33",
      "53D20"
    ],
    "keywords": [
      "critical points",
      "lyapunov stable relative periodic orbits",
      "geometric mechanics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}