{
  "id": "1703.02526",
  "version": "v1",
  "published": "2017-03-07T18:47:48.000Z",
  "updated": "2017-03-07T18:47:48.000Z",
  "title": "Properties of Quasi-Assouad dimension",
  "authors": [
    "Ignacio García",
    "Kathryn Hare"
  ],
  "comment": "13 pages, 2 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "It is shown that for controlled Moran constructions in $\\mathbb{R}$, including the (sub) self-similar and more generally, (sub) self-conformal sets, the quasi-Assouad dimension coincides with the upper box dimension. This can be extended to some special classes of self-similar sets in higher dimensions. The connections between quasi-Assouad dimension and tangents are studied. We show that sets with decreasing gaps have quasi-Assouad dimension $0$ or $1$ and we exhibit an example of a set in the plane whose quasi-Assouad dimension is smaller than that of its projection onto the $x$-axis, showing that quasi-Assouad dimension may increase under Lipschitz mappings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-07T18:47:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "properties",
      "quasi-assouad dimension coincides",
      "upper box dimension",
      "higher dimensions",
      "self-similar sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}