We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space $ℂ{\mathbb{P}}^n$ for every dimension $n\ge 2$ and every degree $d\ge 2$. Precisely, we construct a foliation $ℱ$ which is induced by a homogeneous vector field of degree $d$, has a finite singular set and all the regular leaves are dense in the whole of $ℂ{\mathbb{P}}^n$. Moreover, $ℱ$ satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if $ℱ$ is conjugate to another holomorphic foliation...

We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy contains all the relevant dynamical information, in particular the projective holonomy representations whose topological invariance was conjectured in the eighties by Cerveau and Sad and is proved here under mild hypotheses.