02-187 V. Gelfreich, L. Lerman

Long-periodic orbits and invariant tori in a singularly perturbed Hamiltonian system (2327K, LaTeX) Apr 17, 02

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Abstract. In this paper we study a singularly perturbed two-degrees-of-freedom Hamiltonian system with a normally elliptic slow manifold. We prove that the slow manifold persists but can have a large number ($\sim\eps^{-1}$) of exponentially small ($\le\e^{-c/\eps}$) 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.

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