{
  "id": "2402.03718",
  "version": "v1",
  "published": "2023-12-28T09:52:27.000Z",
  "updated": "2023-12-28T09:52:27.000Z",
  "title": "On symmetries of the IFS attractor",
  "authors": [
    "Genadi Levin"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We notice that the main result of [G.M. Levin, Symmetries on the Julia set, Math. Notes 1990] holds for attractors of holomorphic iterated function systems (IFS) on the plane. Namely, either any non-trivial family of holomorphic local symmetries of the attractor is finite or the attractor contains an analytic arc. In fact, the same holds for any J-like compact subset of the plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-28T09:52:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ifs attractor",
      "holomorphic iterated function systems",
      "holomorphic local symmetries",
      "julia set",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}