{
  "id": "1506.08714",
  "version": "v1",
  "published": "2015-06-29T16:16:46.000Z",
  "updated": "2015-06-29T16:16:46.000Z",
  "title": "Multidimensional self-affine sets: non-empty interior and the set of uniqueness",
  "authors": [
    "Kevin G. Hare",
    "Nikita Sidorov"
  ],
  "comment": "9 pages, no figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $M$ be a $d\\times d$ contracting matrix. In this paper we consider the self-affine iterated function system $\\{Mv-u, Mv+u\\}$, where $u$ is a cyclic vector. Our main result is as follows: if $|\\det M|\\ge 2^{-1/d}$, then the attractor $A_M$ has non-empty interior. We also consider the set $\\mathcal U_M$ of points in $A_M$ which have a unique address. We show that unless $M$ belongs to a very special (non-generic) class, the Hausdorff dimension of $\\mathcal U_M$ is positive. For this special class the full description of $\\mathcal U_M$ is given as well. This paper continues our work begun in [5, 6].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-29T16:16:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80"
    ],
    "keywords": [
      "multidimensional self-affine sets",
      "non-empty interior",
      "uniqueness",
      "self-affine iterated function system",
      "work begun"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150608714H"
    }
  }
}