FM 97-5
V 1.1 (last updated: 12 nov 1997)

Authors: G. Gallavotti, G. Gentile, V. Mastropietro

Title: Pendulum: separatrix splitting 

Abstract: An exact expression for the determinant of
the splitting matrix is derived for three degrees of
freedom systems with three time scales: it allows us to
analyze the asymptotic behaviour needed to amend the
large angles theorem proposed in
Ann. Inst. H. Poincar\'e, B-60, 1, 1994. The asymptotic
validity of Melnikov's integrals is proved for the
class of models considered, which are polynomial
perturbations. The technique for exhibiting
cancellations is inspired by renormalization theory in
quantum electrodynamics and uses an analogue of Dyson's
equations to prove an infinite family of identities,
due to symmetries, that remind us of the Ward's
identities.

Keywords: Arnold diffusion, homoclinic splitting, KAM

G.Ga.: Fisica, Universita' di Roma La Sapienza,
P.le Moro 2, 00185, Roma, Italia.
G.Ge.: Matematica, Universita' di Roma 3,
V.Ma.: Matematica, Universita' di Roma 2, Viale della Ricerca Scientifica, 00133, Roma, Italy.
e-mail giovanni@ipparco.roma1.infn.it
       gentileg@ipparco.roma1.infn.it
       vieri@ipparco.roma1.infn.it
tel. 6-49914370, fax 6-4957697