Memoirs of the American Mathematical Society 2004; 83 pp; softcover Volume: 167 ISBN10: 0821834452 ISBN13: 9780821834459 List Price: US$60 Individual Members: US$36 Institutional Members: US$48 Order Code: MEMO/167/792
 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 nondiagonalizable 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 PoincaréMelnikov function. Readership Graduate students and research mathematicians interested in dynamical systems and ergodic theory. Table of Contents  Notation and main results
 Analytic properties of the homoclinic orbit of the unperturbed system
 Parameterization of local invariant manifolds
 Flow box coordinates
 The extension theorem
 Splitting of separatrices
 References
