Lyapunov 1-form for diffusion processes

We extend the concept of Lyapunov 1-forms for the case of diffu- sion processes to study its asymptotic behavior. We give some examples and a condition for the existence of these objects.

Conditions to the density of accessible sets

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 Kreners theorem.