Key points are not available for this paper at this time.
Let M be a finite dimensional Riemann manifold without boundary. Kupka 5, Sacker Anosov 2 considers perturbations of a nonsingular flow, which of course leaves invariant each leaf of the foliation by trajectories. In both problems there is an assumption of hyperbolicity in planes normal to the submanifold, or trajectories.
Hirsch et al. (Tue,) studied this question.