{
  "id": "2108.05408",
  "version": "v1",
  "published": "2021-08-11T18:51:38.000Z",
  "updated": "2021-08-11T18:51:38.000Z",
  "title": "The Poincaré exponent and the dimensions of Kleinian limit sets",
  "authors": [
    "Jonathan M. Fraser"
  ],
  "comment": "Expository, 6 pages. This article has been accepted for publication in The American Mathematical Monthly, published by Taylor & Francis",
  "categories": [
    "math.DS",
    "math.MG"
  ],
  "abstract": "We provide a proof of the (well-known) result that the Poincar\\'e exponent of a non-elementary Kleinian group is a lower bound for the upper box dimension of the limit set. Our proof only uses elementary hyperbolic and fractal geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-11T18:51:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "30F40"
    ],
    "keywords": [
      "kleinian limit sets",
      "non-elementary kleinian group",
      "upper box dimension",
      "fractal geometry",
      "elementary hyperbolic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}