Complete controllability by piecewise abnormal curves of a generic rank-3 distribution on connected 5- and 6-dimensional manifolds. (Contrôlabilité complète par courbes anormales par moceaux d’une distribution de rang 3 générique sur des variétés connexes de dimension 5 et 6.) (French) Zbl 0899.58003
Authors’ abstract: “We continue the recent note [C. R. Acad. Sci., Paris, Sér. I 322, No. 9, 865-868 (1996; Zbl 0865.58001)] and prove that for a generic rank-3 distribution on a given connected 5- or 6-dimensional \(C^\infty\) manifold every two points can be joined by a piecewise abnormal and \(C^\infty\) curve. In dimension 6 one can fully retrieve such a distribution from the data of its abnormal curves [R. Montgomery, J. Dyn. Control Syst. 1, 49-90 (1995)]. We are able to do the same in dimension 5, not linearly as in Montgomery’s paper for codimension \(\geq 3\) distributions, but in the Lie algebra sense”.
Reviewer: W.Mozgawa (Lublin)
MSC:
| 58A30 | Vector distributions (subbundles of the tangent bundles) |
| 58A35 | Stratified sets |
| 49K15 | Optimality conditions for problems involving ordinary differential equations |
| 37J99 | Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems |
