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 (∼ε−1) of exponentially small (≤e−c/ε) 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.