  Given a control system $\dot{p} = X_0(p) + \sum_i u_i (t)X_i(p)$ on a compact
manifold M we study conditions for the foliation defined by the accessible sets
be dense in M . To do this we relate the control system to a stochastic
differential equation and, using the support theorem, we give a
characterization of the density in terms of the infinitesimal generator of the
diffusion and its invariant measures. Also we give a different proof of
Krener's theorem.
