{
  "id": "2202.06910",
  "version": "v1",
  "published": "2022-02-14T18:02:34.000Z",
  "updated": "2022-02-14T18:02:34.000Z",
  "title": "Equidistribution for matings of quadratic maps with the Modular group",
  "authors": [
    "Vanessa Matus de la Parra"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the asymptotic behavior of the family of holomorphic correspondences $\\lbrace\\mathcal{F}_a\\rbrace_{a\\in\\mathcal{K}}$, given by $$\\left(\\frac{az+1}{z+1}\\right)^2+\\left(\\frac{az+1}{z+1}\\right)\\left(\\frac{aw-1}{w-1}\\right)+\\left(\\frac{aw-1}{w-1}\\right)^2=3.$$ It was proven by Bullet and Lomonaco that $\\mathcal{F}_a$ is a mating between the modular group $\\operatorname{PSL}_2(\\mathbb{Z})$ and a quadratic rational map. We show for every $a\\in\\mathcal{K}$, the iterated images and preimages under $\\mathcal{F}_a$ of nonexceptional points equidistribute, in spite of the fact that $\\mathcal{F}_a$ is weakly-modular in the sense of Dinh, Kaufmann and Wu but it is not modular. Furthermore, we prove that periodic points equidistribute as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-14T18:02:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "modular group",
      "quadratic maps",
      "equidistribution",
      "periodic points equidistribute",
      "nonexceptional points equidistribute"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}