EXTENDED CONVERGENCE OF NORMAL FORMS AROUND UNSTABLE EQUILIBRIA

There is strong numerical evidence that the convergence of normal form s around saddle points of Hamiltonian systems should extend beyond the region originally established by Moser. We show that these normal for ms do converge along a neighbourhood of the stable and unstable manifo lds emanating from Moser's region if the Hamiltonian is analytical. A possible further extension will allow the calculation of homoclinic or bits as intersections of the analytical images of the stable and the u nstable subspaces for the normal form.