Slow manifolds in a singularly perturbed Hamiltonian system

Assume that a Hamiltonian system looses some of its degrees of freedom in the following way: the motion in the slow component stops in the limit epsilon -> 0. In this case, the small parameter enters the dynamics through the corresponding symplectic form instead of the Hamiltonian function. The slow manifold can be defined in the usual way, but unlike the general dissipative case the slow manifold may be normally elliptic even for a generic Hamiltonian. We study a mechanism, which destroys the normally elliptic slow manifold and use a specially developed averaging technique to study the dynamics nearby.