Exponentially Small Splitting of Invariant Manifolds of Parabolic Points

Considers families of one and a half degrees of freedom Hamiltonians with high frequency periodic dependence on time, which are perturbations of an autonomous system. This book supposes that the origin is a parabolic fixed point with non-diagonalizable linear part and that the unperturbed system has a homoclinic connection associated to it.

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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 fixed point with non-diagonalizable linear part and that the unperturbed system has a homoclinic connection associated to it. We provide a set of hypotheses under which the splitting is exponentially small and is given by the Poincare-Melnikov function.