PERSISTENCE OF UNIFORMLY HYPERBOLIC LOWER DIMENSIONAL INVARIANT TORI OF HAMILTONIAN SYSTEMS

Abstract

In this paper, we prove that the normally uniform-hyperbolic lower dimensional invariant tori of the un-perturbed system will persist under small perturbations. The proof is based on the theory of exponentially dichotomous linear systems and an improved KAM machinery adapted for the perturbations of angle dependent unperturbed parts.