{
  "abstract": "Let $\\mathcal{S}_c$ be the subgroup of $Aut(\\mathbb{C}^2)$ generated by affine maps and shear automorphisms with constant Jacobian. We determine the possible conformal types of the rank-one limit set of an invariant recurrent Fatou component when the induced dynamics has infinite order. In particular we show that, under this infinite-order hypothesis, the limit set of a finite composition of Hénon maps (polynomial or transcendental), can only be conformally equivalent to a disk or an annulus. Thus we exclude the remaining three conformal types, i.e. $\\mathbb{D}^*$, $\\mathbb{C}^*$ and $\\mathbb{C}$, from the classification result by Arosio, Benini, Fornæss and Peters. We also prove that the set of fixed points of a finite composition of Hénon maps (polynomial or transcendental) contains no entire curves.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17335",
  "author_total": 1,
  "authors": [
    {
      "name": "Luka Boc Thaler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dhzmz56sec969.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17335",
  "fulltext_url": null,
  "id": "dhzmz56sec969",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17335",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221773478",
  "pdf_url": "https://arxiv.org/pdf/2610.17335",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dhzmz56sec969.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17335",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17335"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "On the rank-one limit sets for maps in the constant-Jacobian shear group of $\\mathbb{C}^2$",
  "title_text": "On the rank-one limit sets for maps in the constant-Jacobian shear group of ℂ^2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/dhzmz56sec969",
  "venue": "arXiv",
  "versions": []
}