{
  "id": "2203.04931",
  "version": "v1",
  "published": "2022-03-09T18:22:19.000Z",
  "updated": "2022-03-09T18:22:19.000Z",
  "title": "The Assouad spectrum of Kleinian limit sets and Patterson-Sullivan measure",
  "authors": [
    "Jonathan M. Fraser",
    "Liam Stuart"
  ],
  "comment": "31 pages, 11 figures. This paper used to form part of arXiv:2007.15493 which has subsequently been cut into three pieces",
  "categories": [
    "math.DS",
    "math.CA",
    "math.MG"
  ],
  "abstract": "The Assouad dimension of the limit set of a geometrically finite Kleinian group with parabolics may exceed the Hausdorff and box dimensions. The Assouad \\emph{spectrum} is a continuously parametrised family of dimensions which `interpolates' between the box and Assouad dimensions of a fractal set. It is designed to reveal more subtle geometric information than the box and Assouad dimensions considered in isolation. We conduct a detailed analysis of the Assouad spectrum of limit sets of geometrically finite Kleinian groups and the associated Patterson-Sullivan measure. Our analysis reveals several novel features, such as interplay between horoballs of different rank not seen by the box or Assouad dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-09T18:22:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "37F32"
    ],
    "keywords": [
      "kleinian limit sets",
      "assouad spectrum",
      "assouad dimension",
      "geometrically finite kleinian group",
      "subtle geometric information"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}