Mathematics

In the classical calculus of variations second order conditions are usually stated using the theory of conjugate points. But there exists a more flexible approach via symplectic geometry, that allows to generalize the notion of a conjugate point to a great variety of constrained variational problems including problems of optimal control. In the talk we are going to discuss basic notions of this theory, motivation and several results on the subject obtained in a joint work with prof. A. Agrachev.