{
  "id": "1504.07138",
  "version": "v1",
  "published": "2015-04-27T15:48:16.000Z",
  "updated": "2015-04-27T15:48:16.000Z",
  "title": "On the dimension of self-affine sets and measures with overlaps",
  "authors": [
    "Balázs Bárány",
    "Michał\\ Rams",
    "Károly Simon"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we consider diagonally affine, planar IFS $\\Phi=\\left\\{S_i(x,y)=(\\alpha_ix+t_{i,1},\\beta_iy+t_{i,2})\\right\\}_{i=1}^m$. Combining the techniques of Hochman and Feng, Hu we compute the Hausdorff dimension of the self-affine attractor and measures and we give an upper bound for the dimension of the exceptional set of parameters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-27T15:48:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "28A78"
    ],
    "keywords": [
      "self-affine sets",
      "planar ifs",
      "hausdorff dimension",
      "self-affine attractor",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150407138B"
    }
  }
}