{
  "id": "math/0202215",
  "version": "v1",
  "published": "2002-02-21T13:19:19.000Z",
  "updated": "2002-02-21T13:19:19.000Z",
  "title": "Hausdorff dimension of the set of extreme points of a self-similar set",
  "authors": [
    "Andrew Tetenov",
    "Ivan Davydkin"
  ],
  "comment": "10 pages, 3 figures, Latex2e",
  "categories": [
    "math.MG",
    "math.DS"
  ],
  "abstract": "If the system S of contracting similitudes on $ R^2$ satisfies open convex set condition, then the set F of extreme points of the convex hull $\\tilde{K}$ of it's invariant self-similar set K has Hausdorff dimension 0 . If, additionally, all the rotation angles of the similitudes are commensurable with $\\pi$, then the set F is finite and the convex hull $\\tilde{K}$ is a convex polygon.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-02-21T13:19:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80"
    ],
    "keywords": [
      "hausdorff dimension",
      "extreme points",
      "satisfies open convex set condition",
      "convex hull",
      "invariant self-similar set"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2215T"
    }
  }
}