Computing Casimir invariants from Pfaffian systems

We describe a method for computing Casimir invariants that is applicable to both finite and infinite-dimensional Poisson brackets. We apply the method to various finite and infinite-dimensional examples, including a Poisson bracket embodying both finite and infinite-dimensional structure

Generalized Hamiltonian structures for Ermakov systems

We construct Poisson structures for Ermakov systems, using the Ermakov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations, the existence of Casimir functions can give rise to superintegrable Ermakov systems. Finally, we characterize the cases where linearization of the equations of motion is possible