{
  "id": "2106.04711",
  "version": "v1",
  "published": "2021-06-08T22:04:32.000Z",
  "updated": "2021-06-08T22:04:32.000Z",
  "title": "On co-$σ$-porosity of the parameters with dense critical orbits for skew tent maps and matching on generalized $β$-transformations",
  "authors": [
    "Henk Bruin",
    "Gabriella Keszthelyi"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that the critical point and the point $1$ have dense orbits for Lebesgue-a.e., parameter pairs in the two-parameter skew-tent family and generalised $\\beta$-transformations. As an application, we show that for the generalised $\\beta$-transformation with the tribonacci number as slope, there is matching (i.e., $T^n(0)=T^n(1)$ for some $n \\geq 1$) for Lebesgue-a.e. translation parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-08T22:04:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E10",
      "11R06",
      "37E05",
      "37E45",
      "37A45"
    ],
    "keywords": [
      "skew tent maps",
      "dense critical orbits",
      "transformation",
      "translation parameter",
      "lebesgue-a"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}