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