{
  "id": "2202.11404",
  "version": "v1",
  "published": "2022-02-23T10:34:57.000Z",
  "updated": "2022-02-23T10:34:57.000Z",
  "title": "Exceptional sets for average conformal dynamical systems",
  "authors": [
    "Congcong Qu",
    "Juan Wang"
  ],
  "comment": "33 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f: M \\to M$ be a $C^{1+\\alpha}$ map/diffeomorphism of a compact Riemannian manifold $M$ and $\\mu$ be an expanding/hyperbolic ergodic $f$-invariant Borel probability measure on $M$. Assume $f$ is average conformal expanding/hyperbolic on the support set $W$ of $\\mu$ and $W$ is locally maximal. For any subset $A\\subset W$ with small entropy or dimension, we investigate the topological entropy and Hausdorff dimensions of the $A$-exceptional set and the limit $A$-exceptional set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-23T10:34:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C45",
      "37B40",
      "37D25",
      "37F35"
    ],
    "keywords": [
      "average conformal dynamical systems",
      "exceptional set",
      "invariant borel probability measure",
      "compact riemannian manifold",
      "average conformal expanding/hyperbolic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}