{
  "abstract": "We study non-autonomous basins of $F_j$ automorphisms of $\\mathbb C^2$ satisfying $$a_j\\|p\\|\\leq\\|F_j(p)\\|\\leq b_j\\|p\\|\\qquad (\\forall p\\in \\mathbb B)$$ where $0<a_j<b_j<b<1$. We show that if $b_j^m<a_j$ for some integer $m$ and all $j>0$ then every bounded plurisubharmonic function on the non-autonomous basin is constant. Moreover, if in addition we have $\\prod_{i=1}^{j-1}b_i\\leq b_j^m$ then the basin is biholomorphic to $\\mathbb C^2$. For the quadratic Hénon family $$F_n(z,w)=\\bigl(z^2+c^{q_n}w,c^{q_n}z\\bigr), \\qquad 0<c<1,$$ we study how the asymptotic behavior of the sequence $q_n\\to\\infty$ influences the complex structure of the basin. In particular, we identify broad regimes in which the non-autonomous basin is either biholomorphic to $\\mathbb C^2$ or is a Short $\\mathbb C^2$, thereby isolating possible sequences for which other complex structures may occur.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00627",
  "author_total": 1,
  "authors": [
    {
      "name": "Luka Boc Thaler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/12ezyaqyg4ets.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00627",
  "fulltext_url": null,
  "id": "12ezyaqyg4ets",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00627",
  "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": "W7216354335",
  "pdf_url": "https://arxiv.org/pdf/2610.00627",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/12ezyaqyg4ets.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00627",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00627"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Complex structures of non-autonomous basins",
  "title_text": "Complex structures of non-autonomous basins",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/12ezyaqyg4ets",
  "venue": "arXiv",
  "versions": []
}