ABSTRACT
Given a control system on a compact manifold M, we study conditions for the foliation defined by the accessible sets to be dense in M. For this, we relate the control system to a stochastic differential equation and, by the support theorem, we give a characterization of the density in terms of the infinitesimal generator of the diffusion and its invariant measures.
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Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1. In fact, compare the construction of the process given with the construction of the Brownian motion given, for example, in [Citation12, pp. 77–78].