Persistence of Invariant Tori in Generalized Hamiltonian Systems

AMS(MOS). Mathematics Subject Classification. 58F05, 58F27, 58F30.We present some results of KAM type, comparable to the KAM theory for volume-preserving maps and flows, for generalized Hamiltonian systems which may admit a distinct number of action and angle variables. In particular, systems under consideration can be odd dimensional. Applications to the perturbation of three dimensional steady Euler fluid particle path flows are considered with respect to the existence problem of barriers to fluid transport and mixing