{
  "id": "1201.0280",
  "version": "v1",
  "published": "2011-12-31T16:09:49.000Z",
  "updated": "2011-12-31T16:09:49.000Z",
  "title": "Symbolic dynamics for the $N$-centre problem at negative energies",
  "authors": [
    "Nicola Soave",
    "Susanna Terracini"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the planar $N$-centre problem, with homogeneous potentials of degree $-\\a<0$, $\\a \\in [1,2)$. We prove the existence of infinitely many collisions-free periodic solutions with negative and small energy, for any distribution of the centres inside a compact set. The proof is based upon topological, variational and geometric arguments. The existence result allows to characterize the associated dynamical system with a symbolic dynamics, where the symbols are the partitions of the $N$ centres in two non-empty sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-31T16:09:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70F10",
      "37N05",
      "70F15",
      "37J30"
    ],
    "keywords": [
      "centre problem",
      "symbolic dynamics",
      "negative energies",
      "collisions-free periodic solutions",
      "non-empty sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.0280S"
    }
  }
}