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Exponentially small splitting of invariant manifolds of parabolic points

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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 xed 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 Poincaré-Melnikov function.

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Memoirs of the American Mathematical Society, 2004, vol. 167, num. 792

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(c) American Mathematical Society (AMS), 2004

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Exponentially small splitting of invariant manifolds of parabolic points