{
  "id": "1112.1789",
  "version": "v1",
  "published": "2011-12-08T09:20:26.000Z",
  "updated": "2011-12-08T09:20:26.000Z",
  "title": "Global dynamics of stationary, dihedral, nearly-parallel vortex filaments",
  "authors": [
    "Francesco Paparella",
    "Alessandro Portaluri"
  ],
  "comment": "28 pages, 11 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "The goal of this paper is to give a detailed analytical description of the global dynamics of N points interacting through the singular logarithmic potential and subject to the following symmetry constraint: at each instant they form an orbit of the dihedral group of order 2l. The main device in order to achieve our results is a technique very popular in Celestial Mechanics, usually referred to as \"McGehee transformation\". After performing this change of coordinates that regularizes the total collision, we study the rest-points of the flow, the invariant manifolds and we derive interesting information about the global dynamics for l=2. We observe that our problem is equivalent to studying the geometry of stationary configurations of nearly-parallel vortex filaments in three dimensions in the LIA approximation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-08T09:20:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70F10",
      "37C80"
    ],
    "keywords": [
      "nearly-parallel vortex filaments",
      "global dynamics",
      "singular logarithmic potential",
      "stationary configurations",
      "invariant manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.1789P"
    }
  }
}