Invariant sets near singularities of holomorphic foliations

Abstract

Consider a complex one dimensional foliation on a complex surface near a singularity $p$. If $\mathcal{I}$ is a closed invariant set containing the singularity $p$, then $\mathcal{I}$ contains either a separatrix at $p$ or an invariant real three dimensional manifold singular at $p$.

Cited by in corpus (4)

• Meromorphic vector fields with single-valued solutions on complex surfaces
• Partial separatrices and local Brunella's alternative
• On the dynamics of foliations in ${\mathbb{P}}^n$ tangent to Levi-flat hypersurfaces
• Invariant Hypersurfaces and Nodal Components of Foliations