{
  "id": "2403.18612",
  "version": "v1",
  "published": "2024-03-27T14:28:01.000Z",
  "updated": "2024-03-27T14:28:01.000Z",
  "title": "Bowen's formula for a rational graph-directed Markov system",
  "authors": [
    "Tadashi Arimitsu",
    "Johannes Jaerisch",
    "Hiroki Sumi",
    "Takayuki Watanabe"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We establish Bowen's formula for the Julia set of a non-elementary, expanding, irreducible and aperiodic rational graph-directed Markov system satisfying the backward separating condition. Towards this end, we shall prove that the associated skew product map is topologically exact on the skew product Julia set, and satisfies the density of repelling periodic points. Moreover, we give a criterion for expandingness in terms of hyperbolicity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-27T14:28:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "58F23",
      "30D05",
      "37H12"
    ],
    "keywords": [
      "bowens formula",
      "graph-directed markov system satisfying",
      "skew product julia set",
      "aperiodic rational graph-directed markov system",
      "associated skew product map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}