{
  "annotation_id": "e66ea201-ec72-4d06-830a-1bf7e547f79a",
  "date_created": "2026-02-17T05:53:12.483000Z",
  "date_modified": "2026-02-17T05:53:12.483000Z",
  "file_hash": "64f9a687c52c206a4a04cfa7854e3aac1f73079ce5b4d00e9a7fa5c0b6cae0ef",
  "private": false,
  "record": {
    "abstract": "Let $H$ be a polynomial automorphism of $\\mathbb{C}^2$ of positive entropy and degree $d \\ge 2$. We prove that the escaping set $U^+$ (or equivalently, the non-escaping set $K^+$), of $H$ is rigid under the action of holomorphic automorphisms of $\\mathbb{C}^2$. Specifically, every holomorphic automorphism of $\\mathbb{C}^2$ that preserves $U^+$ takes the form $L \\circ H^s$ where $s \\in \\mathbb{Z}$ and $L$ belongs to a finite cyclic group of affine maps that preserve the escaping set.\n  Second, note that the sub-level sets $\\{G^+ \u003c c\\}$, $c \u003e 0$, of the Greens function $G^+$ associated with the map $H$ are canonical examples of Short $\\mathbb{C}^2$s. As a consequence of the above theorem, we show that the holomorphic automorphisms of these Short $\\mathbb{C}^2$s are affine automorphisms of $\\mathbb{C}^2$ preserving the escaping set $U^+$. Hence, the automorphism group of these Short $\\mathbb{C}^2$s are the same for every $c\u003e0$ and is a finite cyclic group.",
    "arxiv_id": "2601.07681",
    "authors": [
      "Sayani Bera",
      "Kaushal Verma"
    ],
    "categories": [
      "math.CV",
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "title": "Rigidity of the escaping set of polynomial automorphisms of $\\mathbb{C}^2$",
    "url": "https://arxiv.org/abs/2601.07681",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9ef5f646-7d9e-4ea3-89a2-c60d1bbf531b",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}