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PreprintCC BY 4.0arXiv

Structural stability of the Jouanolou foliations in every degree

  • Sahil Gehlawat
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Abstract

We show that the degree d Jouanolou foliation π’₯d on β„™2 is structurally stable for every d β‰₯ 2. We prove the existence of a neighbourhood 𝒰d of π’₯d, such that every foliation β„± ∈ 𝒰d 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 β„™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 β‰₯ 2.

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Cite

BibTeXRIS
BibTeX
@misc{gehlawat2026structural,
  title = {{Structural stability of the Jouanolou foliations in every degree}},
  author = {Sahil Gehlawat},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35597},
  eprint = {2609.35597},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35597},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Structural stability of the Jouanolou foliations in every degree
AU  - Sahil Gehlawat
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35597
UR  - https://arxiv.org/abs/2609.35597
AB  - We show that the degree d Jouanolou foliation π’₯_d on β„™^2 is structurally stable for every d β‰₯ 2. We prove the existence of a neighbourhood 𝒰_d of π’₯_d, such that every foliation β„± ∈ 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 β„™^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 β‰₯ 2.
ER  -