We consider families of one and a half degrees of freedom Hamiltonians with
high frequency periodic dependence on time, which are perturbations of an au-
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.
Received by the editor April 15, 2002.
2000 Mathematics Subject Classification. Primary 37J45; Secondary 70K44, 34C37, 34E10,
The authors thank the support of the Catalan Grant CIRIT 2001SGR-70.
The second author also thanks the partial support of the Spanish Grant DGICYT BFM2000-
0805 and the INTAS project 00-221.