Lecturer(s)


SERGYEYEV Artur, doc. RNDr. Ph.D.

Course content

 Jets of differentiable mappings, fiber bundles and their prolongations, manifolds of contact elements  The Lagrange structures (horizontal and contact forms, Lepagean forms, the first variation formula, the EulerLagrange equations, the Hamilton equations)  Symmetries of the Lagrange structures (invariance transformations of the Lagrange structure, generalized symmetries, the first Noether theorem, the natural Lagrange structures, the second Noether theorem)  The field of extremals and the HamiltonJacobi equations  Foundations of the theory of bundles, variational sequence.

Learning activities and teaching methods

unspecified

Recommended literature


D. Krupka. Jets and Contact Elements. Proc. of the Seminar on Differential Geometry, Mathematical Publications. Silesian University, Opava, 2000.

D. Krupka. The Geometry of Lagrange Structures II.  Elementary Sheaf Theory. Silesian University, Opava, 1998.

D. Krupka. The Geometry of Lagrange Structures. Silesian University, Opava, 1997.

I. M. Gelfand, S. V. Fomin. Calculus of Variations. Englewood Cliffs, PrenticeHall, 1963.

P.J. Olver. Applications of Lie groups to differential equations. 1993.
