{
  "id": "1712.07353",
  "version": "v1",
  "published": "2017-12-20T07:52:27.000Z",
  "updated": "2017-12-20T07:52:27.000Z",
  "title": "Hausdorff dimension of planar self-affine sets and measures",
  "authors": [
    "Balázs Bárány",
    "Michael Hochman",
    "Ariel Rapaport"
  ],
  "comment": "47 pages, 2 figures",
  "categories": [
    "math.MG",
    "math.DS"
  ],
  "abstract": "Let $X=\\bigcup\\varphi_{i}X$ be a strongly separated self-affine set in $\\mathbb{R}^2$ (or one satisfying the strong open set condition). Under mild non-compactness and irreducibility assumptions on the matrix parts of the $\\varphi_{i}$, we prove that $\\dim X$ is equal to the affinity dimension, and similarly for self-affine measures and the Lyapunov dimension. The proof is via analysis of the dimension of the orthogonal projections of the measures, and relies on additive combinatorics methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-20T07:52:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "37C45",
      "37F35"
    ],
    "keywords": [
      "planar self-affine sets",
      "hausdorff dimension",
      "strong open set condition",
      "orthogonal projections",
      "strongly separated self-affine set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}