{
  "id": "1308.5578",
  "version": "v1",
  "published": "2013-08-26T13:22:18.000Z",
  "updated": "2013-08-26T13:22:18.000Z",
  "title": "Minimizing configurations and Hamilton-Jacobi equations of homogeneous N-body problems",
  "authors": [
    "Ezequiel Maderna"
  ],
  "categories": [
    "math.DS",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "For $N$-body problems with homogeneous potentials we define a special class of central configurations related with the reduction of homotheties in the study of homogeneous weak KAM solutions. For potentials in $1/r^\\alpha$ with $\\alpha\\in (0,2)$ we prove the existence of homogeneous weak KAM solutions. We show that such solutions are related to viscosity solutions of another Hamilton-Jacobi equation in the sphere of normal configurations. As an application we prove for the Newtonian three body problem that there are no smooth homogeneous solutions to the critical Hamilton-Jacobi equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-26T13:22:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D40",
      "70F10"
    ],
    "keywords": [
      "hamilton-jacobi equation",
      "homogeneous n-body problems",
      "homogeneous weak kam solutions",
      "minimizing configurations",
      "viscosity solutions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1134/S1560354713060063",
      "journal": "Regular and Chaotic Dynamics",
      "year": 2013,
      "month": "Nov",
      "volume": 18,
      "number": 6,
      "pages": 656
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013RCD....18..656M"
    }
  }
}