Long-periodic orbits and invariant tori in a singularly perturbed Hamiltonian system

In this paper, we study a singularly perturbed, two-degree-of-freedom Hamiltonian system with a normally elliptic slow manifold. We prove that the slow manifold persists but can have a large number (similar toepsilon(-1)) of exponentially small (less than or equal toe(-c/epsilon)) gaps. We demonstrate the existence of KAM tori in a neighborhood of the slow manifold. In addition, we investigate a bifurcation which describes the creation of a gap in the slow manifold and derive its normal form. (C) 2002 Elsevier Science B.V. All rights reserved.