{
  "id": "1010.0881",
  "version": "v1",
  "published": "2010-10-05T13:33:12.000Z",
  "updated": "2010-10-05T13:33:12.000Z",
  "title": "Differentiability of fractal curves",
  "authors": [
    "Christoph Bandt",
    "Alexey Kravchenko"
  ],
  "doi": "10.1088/0951-7715/24/10/003",
  "categories": [
    "math.DS",
    "math.MG"
  ],
  "abstract": "While self-similar sets have no tangents at any single point, self-affine curves can be smooth. We consider plane self-affine curves without double points and with two pieces. There is an open subset of parameter space for which the curve is differentiable at all points except for a countable set. For a parameter set of codimension one, the curve is continuously differentiable. However, there are no twice differentiable self-affine curves in the plane, except for parabolic arcs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-05T13:33:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "26A27"
    ],
    "keywords": [
      "fractal curves",
      "differentiability",
      "twice differentiable self-affine curves",
      "plane self-affine curves",
      "open subset"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Nonlinearity",
      "year": 2011,
      "month": "Oct",
      "volume": 24,
      "number": 10,
      "pages": 2717
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011Nonli..24.2717B"
    }
  }
}