Locally hamiltonian systems with symmetry and a generalized Noether's theorem

Abstract

An analysis of global aspects of the theory of symmetry groupsG of locally Hamiltonian dynamical systems is carried out for particular cases either of the symmetry group, or the differentiable manifoldM supporting the symplectic structure, or the action ofG onM. In every case we obtain a generalization of Noether's theorem. We also look at the classical Noether's theorem for Lagrangian systems from a modern perspective.