Structural stability of the Jouanolou foliation of degree 2

2023/03/16 by Aurélien Alvarez, Alvarez, Aurélien, Bertrand Deroin +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2303.09313

openalex publication_date 2023/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Jouanolou foliation of degree 2 on the complex projective plane is structurally stable. Moreover, its Fatou set is a fibration on the Klein quartic with the structure of a smooth fiber bundle in disks. In particular, there is no dense leaf.

Related

• Arithmetic aspects of the Jouanolou foliation
• Existence and stability of foliations by J-holomorphic spheres
• Non-algebraicity of foliations via reduction modulo 2
• Compact leaves of codimension one holomorphic foliations on projective\n manifolds
• Stability of branched pull-back projective foliations