TITLE: Exponentially small splitting of separatrices in a
weakly hyperbolic case

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 validate the Poincare-Melnikov method in the singular case of high-frequency
periodic perturbations of the Hamiltonian h(x, y) = (1/2)y^2 - x^3 + x^4 under
appropriate conditions, which among other things, imply that we are considering
the bifurcation case when the character of the fixed point changes from
parabolic in the unperturbed case to hyperbolic in the perturbed one. The
splitting is exponentially small.