{
  "id": "2311.06014",
  "version": "v1",
  "published": "2023-11-10T11:56:02.000Z",
  "updated": "2023-11-10T11:56:02.000Z",
  "title": "Hausdorff dimension of the set of eventually always hitting points on a self-conformal set",
  "authors": [
    "Xintian Zhang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Recurrence problems are fundamental in dynamics, and for example, sizes of the set of points recurring infinitely often to a target have been studied extensively in many contexts. For example, the shrinking target set in iterated function system is an active research area recently. In the current work, we consider a set with a finer recurrence quality, the eventually always hitting set. In a sense, the points in the intersection of an eventually always hitting set and a shrinking target set not only return infinitely often but also at a bounded rate. We study this set in the context of self-conformal iterated function systems, and compute upper and lower bounds for its Hausdorff dimension. Additionally, as an intermediate theorem, we obtain a Hausdorff dimension result for the intersection of eventually always hitting and shrinking target sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-10T11:56:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C45",
      "28A80"
    ],
    "keywords": [
      "shrinking target set",
      "self-conformal set",
      "hitting points",
      "hausdorff dimension result",
      "finer recurrence quality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}