A.Ushakov (SPbGU)

Non-symplectic generalizations and variational principles of Hamiltonian mechanics.

The report is dedicated to generalizations of Hamiltonian mechanics, which allow us to include into consideration the so called "non-Lagrange" systems. The following items are considered: different deformations of Poissons brackets; generalized Fedosov manifolds in the case of non-symplectic manifolds; the system "charged particle in the field of magnetic monopole"; formulation of covariant variational principle; the construction of variational principle in the case of inexact symplectic forms.