{
  "id": "2305.03426",
  "version": "v1",
  "published": "2023-05-05T10:54:26.000Z",
  "updated": "2023-05-05T10:54:26.000Z",
  "title": "The R-IFSs and their attractors",
  "authors": [
    "Hung Nguyen Viet",
    "Duy Mai The",
    "Thanh Vu Thi Hong"
  ],
  "comment": "11 pages, 4 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "This paper introduces a new class of iterated function systems (IFSs) called R-IFSs, which include both rotation/reflection maps and contraction maps. The study of R-IFSs is motivated by the recent research direction on enriching IFSs by adding other types of mappings. The paper investigates the existence and properties of the semi-attractor and compact invariant sets of R-IFSs, as well as the class of minimal invariant sets of R-IFSs. The paper also provides a familiar setting that is an invariant set of R-IFS but not an invariant set of any IFS.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-05T10:54:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "attractors",
      "minimal invariant sets",
      "compact invariant sets",
      "rotation/reflection maps",
      "contraction maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}