  A holomorphic foliation $\mathscr{F}$ on a compact complex manifold $M$ is
said to be an $\mathscr{L}$-foliation if there exists an action of a complex
Lie group $G$ such that the generic leaf of $\mathscr{F}$ coincides with the
generic orbit of $G$. We study $\mathscr{L}$-foliations of codimension one, in
particular in projective space, in the spirit of classical invariant theory,
but here the invariants are sometimes transcendantal ones. We give a bestiary
of examples and general properties. Some classification results are obtained in
low dimensions.

Dynamical Systems