Conditions to the density of accessible sets

Abstract

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.

arXiv commentThis paper has been withdrawn by the author due to crucial error in theorem 3. The equivalence stated here is wrong. The gap in the proof is on p. 5, paragraph starting with "On the other side"