02-166 I. Baldom , E. Fontich

Exponentially small splitting of invariant manifolds of parabolic points. (898K, postscript) Apr 3, 02

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Abstract. We consider families of one and a half degrees of freedom Hamiltonians with high frequency periodic dependence on time, which are perturbations of an autonomous system. We suppose that the origin is a parabolic fixed point with non-diagonalizable linear part and that the unperturbed system has a homoclinic connexion associated to it. We provide a set of hypotheses under which the splitting is exponentially small and is given by the Poincar -Melnikov function.

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