Singularities of the Hamiltonian Vectorfield in Optimal Control Problems

Variational problems with n degrees of freedom give rise Žby the Pontriaguine maximum principle. to a hamiltonian vectorfield in T* n, that presents singularitiesŽnon- smoothness points.when the lagrangean is not convex. For the problems of the calculus of variations, the singularities that occur are points where the hamiltonian vectorfield is not C0. For optimal control problems, we show that besides these singularities there appear other ones: points where the hamiltonian vectorfield is C0 but not C1, and we classify them.