{
  "id": "2011.02756",
  "version": "v1",
  "published": "2020-11-05T10:57:11.000Z",
  "updated": "2020-11-05T10:57:11.000Z",
  "title": "Invariant escaping Fatou components with two rank 1 limit functions for automorphisms of $\\mathbb{C}^2$",
  "authors": [
    "Anna Miriam Benini",
    "Alberto Saracco",
    "Michela Zedda"
  ],
  "comment": "16 pages",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We construct automorphisms of $\\mathbb{C}^2$, and more precisely transcendental H\\'enon maps, with an invariant escaping Fatou component which has exactly two distinct limit functions, both of (generic) rank 1. We also prove a general growth lemma for the norm of points in orbits belonging to invariant escaping Fatou components for automorphisms of the form $F(z,w)=(g(z,w),z)$ with $g(z,w):\\mathbb{C}^2\\rightarrow\\mathbb{C}$ holomorphic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-05T10:57:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F80",
      "32H50",
      "37F10"
    ],
    "keywords": [
      "invariant escaping fatou component",
      "automorphisms",
      "general growth lemma",
      "precisely transcendental henon maps",
      "distinct limit functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}