{
  "id": "2311.07305",
  "version": "v1",
  "published": "2023-11-13T12:49:57.000Z",
  "updated": "2023-11-13T12:49:57.000Z",
  "title": "Weak expansion properties and a large deviation principle for coarse expanding conformal systems",
  "authors": [
    "Zhiqiang Li",
    "Hanyun Zheng"
  ],
  "comment": "38 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we prove that for a metric coarse expanding conformal system $f\\:(\\mathfrak{X}_1,X)\\rightarrow (\\mathfrak{X}_0,X)$ with repellor $X$, the map $f|_X\\:X\\rightarrow X$ is asymptotically $h$-expansive. Moreover, we show that $f|_X$ is not $h$-expansive if there exists at least one branch point in the repellor. As a consequence of asymptotic $h$-expansiveness, for $f|_X$ and each real-valued continuous potential on $X$, there exists at least one equilibrium state. For such maps, if some additional assumptions are satisfied, we can furthermore establish a level-2 large deviation principle for iterated preimages, followed by an equidistribution result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-13T12:49:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37D35",
      "37F20",
      "37F15",
      "37D25",
      "37B99",
      "57M12"
    ],
    "keywords": [
      "large deviation principle",
      "weak expansion properties",
      "metric coarse expanding conformal system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}