Invariant sets near singularities of holomorphic foliations

César Camacho, Rudy Rosas

Published 2013-12-03Version 1

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 $p$.