Minimality: any leaf (curve) is dense in $\Bbb C\Bbb P^n$.

Ergodicity: any Lebesgue measurable subset of leaves has zero or total Lebesgue measure.

Entropy: the topological entropy is strictly positive even far from singularities.

Rigidity: if $\Cal F$ is conjugate to some $\Cal F'\in\Cal U$ by a homeomorphism close to the identity, then they are also conjugate by a projective transformation.

The main analytic tool employed in the construction of these foliations is the existence of several pseudo-flows in the closure of pseudo-groups generated by perturbations of elements in $\text{Diff}(\Bbb C^n,0)$ on a fixed ball.