Some basic properties of infinite dimensional Hamiltonian systems

Chernoff, P. R. and J. E. Marsden

Colloq. Intern., 237, 313-330

Abstract:

We consider some fundamental properties of infinite dimensional Hamiltonian systems, both linear and nonlinear. For example, in the case of linear systems, we prove a symplectic version of the theorem of M. Stone. In the general case, we establish conservation of energy and the moment function for system with symmetry. (The moment function was introduced by B. Kostant and J. M. Souriau). For infinite dimensional systems these conservation laws are more delicate than those for finite dimensional systems because we are dealing with partial as opposed to ordinary differential equations.