{
  "id": "0809.0150",
  "version": "v1",
  "published": "2008-08-31T20:24:37.000Z",
  "updated": "2008-08-31T20:24:37.000Z",
  "title": "Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions",
  "authors": [
    "Aris Daniilidis",
    "Olivier Ley",
    "Stéphane Sabourau"
  ],
  "journal": "Journal de Math\\'ematiques Pures et Appliqu\\'es 94 (2010) 183-199",
  "doi": "10.1016/j.matpur.2010.03.007",
  "categories": [
    "math.DS",
    "math.OC"
  ],
  "abstract": "We hereby introduce and study the notion of self-contracted curves, which encompasses orbits of gradient systems of convex and quasiconvex functions. Our main result shows that bounded self-contracted planar curves have a finite length. We also give an example of a convex function defined in the plane whose gradient orbits spiral infinitely many times around the unique minimum of the function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-31T20:24:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C10",
      "34D20",
      "37B35",
      "37N40",
      "52A10"
    ],
    "keywords": [
      "asymptotic behaviour",
      "main result",
      "bounded self-contracted planar curves",
      "finite length",
      "gradient systems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.0150D"
    }
  }
}