VARIATIONAL-PRINCIPLES AND POISSON STRUCTURES

In previous work we claimed that there is a correspondence between the variational and Poisson formalisms. This claim is valid only locally. For degenerate fundamental 2-forms or non-trivial Poisson manifolds, there are basic differences in the geometry of these two approaches. This does not arise in the non-degenerate case of a symplectic manifold. We qualify the claims made previously and illustrate with examples.