{
  "id": "2401.03953",
  "version": "v1",
  "published": "2024-01-08T15:20:42.000Z",
  "updated": "2024-01-08T15:20:42.000Z",
  "title": "Multifractal analysis for the pointwise Assouad dimension of self-similar measures",
  "authors": [
    "Roope Anttila",
    "Ville Suomala"
  ],
  "comment": "22 pages, 1 figure. Comments are welcome!",
  "categories": [
    "math.DS",
    "math.CA"
  ],
  "abstract": "We quantify the pointwise doubling properties of self-similar measures using the notion of pointwise Assouad dimension. We show that all self-similar measures satisfying the open set condition are pointwise doubling in a set of full Hausdorff dimension, despite the fact that they can in general be non-doubling in a set of full Hausdorff measure. More generally, we carry out multifractal analysis by determining the Hausdorff dimension of the level sets of the pointwise Assouad dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-08T15:20:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "37C45"
    ],
    "keywords": [
      "pointwise assouad dimension",
      "self-similar measures",
      "multifractal analysis",
      "full hausdorff dimension",
      "full hausdorff measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}