G. Gallavotti, G. Gentile, V. Mastropietro
Pendulum: separatrix splitting
(125K, TeX (to print the figure complie with dvips, 1 figure, 30 pages))

ABSTRACT.  An exact expression for the determinant of the
splitting matrix is derived: it allows us to analyze the
asympotic behaviour needed to amend the large angles
theorem proposed in {\rm Ann. Inst. H. Poincar\'e, B-60,
1, 1994}. The asymtotic validity of Melnikov's formulae
is proved for the class of models considered, which
include polynomial perturbations.