{
  "id": "0903.2216",
  "version": "v3",
  "published": "2009-03-12T17:08:43.000Z",
  "updated": "2009-10-21T14:07:55.000Z",
  "title": "The Hausdorff dimension of the projections of self-affine carpets",
  "authors": [
    "Andrew Ferguson",
    "Thomas Jordan",
    "Pablo Shmerkin"
  ],
  "comment": "20 pages. Some minor errors have been corrected and a few points have been clarified",
  "journal": "Fund. Math. 209 (2010), no. 3, 193--213",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the orthogonal projections of a large class of self-affine carpets, which contains the carpets of Bedford and McMullen as special cases. Our main result is that if $\\Lambda$ is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of $\\Lambda$ in a non-principal direction has Hausdorff dimension $\\min(\\gamma,1)$, where $\\gamma$ is the Hausdorff dimension of $\\Lambda$. This generalizes a recent result of Peres and Shmerkin on sums of Cantor sets.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-10-21T14:07:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "28A78"
    ],
    "keywords": [
      "hausdorff dimension",
      "self-affine carpets",
      "natural irrationality conditions hold",
      "orthogonal projection",
      "special cases"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.2216F"
    }
  }
}