Invariant hyperbolic tori for Hamiltonian systems with Russmann nondegeneracy conditions

Following the procedure designed by Graff for proving the persistence theorem of invariant hyperbolic tori for Hamiltonian systems with some modifications, we obtain in this paper a KAM theorem for Hamiltonian systems with hyperbolic fixed point. Because the Hamiltonian of unperturbed systems satisfies the Russmann nondegeneracy condition, this generalizes the well-known result of Graff.