{
  "id": "2405.19123",
  "version": "v1",
  "published": "2024-05-29T14:30:06.000Z",
  "updated": "2024-05-29T14:30:06.000Z",
  "title": "Torus diffeomorphisms with parabolic and non-proper actions on the fine curve graph and their generalized rotation sets",
  "authors": [
    "Nastaran Einabadi"
  ],
  "comment": "26 pages, 8 figures",
  "categories": [
    "math.DS",
    "math.GR",
    "math.GT"
  ],
  "abstract": "We prove that a generic element of the Anosov-Katok class of the torus, $\\overline{\\mathcal{O}}^{\\infty}(\\mathbb{T}^2)$, acts parabolically and non-properly on the fine curve graph $C^{\\dagger}(\\mathbb{T}^2)$. Additionally, we show that a generic element of $\\overline{\\mathcal{O}}^{\\infty}(\\mathbb{T}^2)$ admits generalized rotation sets of any point-symmetric compact convex homothety type in the plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-29T14:30:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fine curve graph",
      "generalized rotation sets",
      "torus diffeomorphisms",
      "non-proper actions",
      "point-symmetric compact convex homothety type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}