TITLE: Exponentially Small Splitting of Invariant Manifolds of Parabolic Points AUTHORS: Inmaculada Baldoma, Ernest Fontich. Universitat de Barcelona Departament de Matematica Aplicada i Analisi Gran Via 585, 08007 Barcelona, Spain E-mails: immaculada.baldoma@upc.edu, fontich@ub.edu 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 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.