We give a topological criterion for the minimality of the strong unstable (or stable) foliation of robustly transitive
partially hyperbolic diffeomorphisms.
As a consequence we prove that, for $3$-manifolds, there is an open and dense subset of robustly transitive
diffeomorphisms (far from homoclinic tangencies) such that either the strong stable or the strong unstable foliation is
robustly minimal.
We also give a topological condition (existence of a central periodic compact leaf) guaranteeing (for an open and dense
subset) the simultaneous minimality of the two strong foliations.
AMS 2000 Mathematics subject classification: Primary 37D25; 37C70; 37C20; 37C29
