Dynamical aspects of holomorphic foliations with ample normal bundle

I will discuss the following recent result that was conjectured by Brunella:

Let $X$ be a compact complex manifold of dimension $\geq 3$. Let $\mathcal{F}$ be a codimension one holomorphic foliation on $X$ with ample normal bundle. Then every leaf of $\mathcal{F}$ accumulates to the singular set of $\mathcal{F}$. This result was obtained in collaboration with M. Adachi.