On the stabilization problem for nonholonomic distributions
Let be a smooth connected complete manifold of dimension , and be a smooth nonholonomic distribution of rank on . We prove that if there exists a smooth Riemannian metric on1for which no nontrivial singular path is minimizing, then there exists a smooth repulsive stabilizing section of on . Moreover, in dimension three, the assumption of the absence of singular minimizing horizontal paths can be dropped in the Martinet case. The proofs are based on the study, using specific results of...