On the moment map for smooth and discrete Hamiltonian systems
Seminar Room 1, Newton Institute
The talk concerns Hamiltonian systems with a Lie group symmetry, that are conjugate to a variational problem. The motivation for the talk includes recent results of the speaker with Tania Goncalves, which show the structure of the set of conservation laws arising from Noether's Theorem in terms of invariants and a moving frame. We exhibit a simple explicit formula for the moment map for the related Hamiltonian system, in both smooth and discrete cases, and discuss the application of the Fels and Olver reformulation of the moving frame to the integration problem.