{
  "id": "2208.00546",
  "version": "v1",
  "published": "2022-08-01T00:12:50.000Z",
  "updated": "2022-08-01T00:12:50.000Z",
  "title": "Interior Dynamics of Fatou Sets",
  "authors": [
    "Mi Hu"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we investigate the precise behavior of orbits inside attracting basins. Let $f$ be a holomorphic polynomial of degree $m\\geq2$ in $\\mathbb{C}$, $\\mathcal {A}(p)$ be the basin of attraction of an attracting fixed point $p$ of $f$, and $\\Omega_i (i=1, 2, \\cdots)$ be the connected components of $\\mathcal{A}(p)$. We prove that there is a constant $C$ so that for every point $z_0$ inside any $\\Omega_i$, there exists a point $q\\in \\cup_k f^{-k}(p)$ inside $\\Omega_i$ such that $d_{\\Omega_i}(z_0, q)\\leq C$, where $d_{\\Omega_i}$ is the Kobayashi distance on $\\Omega_i.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-01T00:12:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fatou sets",
      "interior dynamics",
      "orbits inside attracting basins",
      "holomorphic polynomial",
      "precise behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}