{
  "id": "2211.14251",
  "version": "v1",
  "published": "2022-11-25T17:30:01.000Z",
  "updated": "2022-11-25T17:30:01.000Z",
  "title": "On the local connectivity of attractors of Markov IFS",
  "authors": [
    "Nicolae Mihalache"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove an extension of M. Hata's theorem [4] for planar Markov Iterated Function Systems satisfying a strong version of the Open Set Condition. More precisely, if the attractor of such a system is connected, then it is locally connected. We construct counterexamples to show that all additional hypothesis are necessary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-25T17:30:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37B99"
    ],
    "keywords": [
      "local connectivity",
      "markov ifs",
      "planar markov iterated function systems",
      "open set condition",
      "hatas theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}