{
  "abstract": "We show that the degree $d$ Jouanolou foliation $\\mathcal J_d$ on $\\mathbb P^2$ is structurally stable for every $d \\geq 2$. We prove the existence of a neighbourhood $\\mathcal U_d$ of $\\mathcal J_d$, such that every foliation $\\mathcal F \\in \\mathcal U_d$ satisfies: the Fatou set is a connected disc bundle over a compact Riemann surface of genus $d(d+1)/2$, no leaf is dense in $\\mathbb P^2$, and all but countably many regular leaves are biholomorphic to the unit disc. Finally, we prove transverse perfectness of the Julia set on the regular locus for $d \\geq 2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35597",
  "author_total": 1,
  "authors": [
    {
      "name": "Sahil Gehlawat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/01zbq9rp9z54m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35597",
  "fulltext_url": null,
  "id": "01zbq9rp9z54m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35597",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7214770636",
  "pdf_url": "https://arxiv.org/pdf/2609.35597",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/01zbq9rp9z54m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35597",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35597"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Structural stability of the Jouanolou foliations in every degree",
  "title_text": "Structural stability of the Jouanolou foliations in every degree",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/01zbq9rp9z54m",
  "venue": "arXiv",
  "versions": []
}