{
  "id": "2311.10262",
  "version": "v1",
  "published": "2023-11-17T01:07:52.000Z",
  "updated": "2023-11-17T01:07:52.000Z",
  "title": "On the dimension of limit sets on $\\mathbb{P}(\\mathbb{R}^3)$ via stationary measures: variational principles and applications",
  "authors": [
    "Yuxiang Jiao",
    "Jialun Li",
    "Wenyu Pan",
    "Disheng Xu"
  ],
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "In this article, we establish the variational principle of the affinity exponent of Borel Anosov representations. We also establish such a principle of the Rauzy gasket. In Li-Pan-Xu, they obtain a dimension formula of the stationary measures on $\\mathbb{P}(\\mathbb{R}^3)$. Combined with our result, it allows us to study the Hausdorff dimension of limit sets of Anosov representations in $\\mathrm{SL}_3(\\mathbb{R})$ and the Rauzy gasket. It yields the equality between the Hausdorff dimensions and the affinity exponents in both settings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-17T01:07:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary measures",
      "limit sets",
      "variational principle",
      "hausdorff dimension",
      "rauzy gasket"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}