Persistence of Hyperbolic Invariant Tori for Hamiltonian Systems

A perturbation problem for hyperbolic invariant tori is considered, and a KAM type theorem about the existence of invariant tori is proved. In particular, the unperturbed system considered may admit the different dimensions of action and angle variables, and hence this generalizes the works of Graff, Zehnder, Hermann, and Parasyuk.