{
  "id": "2406.19252",
  "version": "v1",
  "published": "2024-06-27T15:21:30.000Z",
  "updated": "2024-06-27T15:21:30.000Z",
  "title": "Critical exponents and dimension for generalised limit sets",
  "authors": [
    "Tianyi Feng",
    "Jonathan M. Fraser"
  ],
  "comment": "16 pages",
  "categories": [
    "math.MG",
    "math.DS"
  ],
  "abstract": "There is a beautiful and well-studied relationship between the Poincare exponent and the fractal dimensions of the limit set of a Kleinian group. Motivated by this, given an arbitrary discrete subset of the unit ball we define a critical exponent and investigate how it relates to the fractal dimensions of the associated generalised limit set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-27T15:21:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical exponent",
      "fractal dimensions",
      "arbitrary discrete subset",
      "kleinian group",
      "poincare exponent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}