MULTI-BUMP ORBITS HOMOCLINIC TO RESONANCE BANDS

We establish the existence of several classes of multi-bump orbits hom oclinic to resonance bands for completely-integrable Hamiltonian syste ms subject to small-amplitude Hamiltonian or dissipative perturbations . Each bump is a fast excursion away from the resonance band, and the bumps are interspersed with slow segments near the resonance band. The homoclinic orbits, which include multi-bump Silnikov orbits, connect equilibria and periodic orbits in the resonance band. The main tools w e use in the existence proofs are the exchange lemma with exponentiall y small error and the existence theory of orbits homoclinic to resonan ce bands which make only one fast excursion away from the resonance ba nds.