Patrick BERNARD
Homoclinic orbits in families of hypersurfaces with hyperbolic periodic 
orbits.
(57K, Latex 2e with PS figure)

ABSTRACT.  We consider a Hamiltonian system in C^n having an invariant plane 
with harmonic oscillations on it. We assume that this plane is 
hyperbolic, which means that the oscillations are hyperbolic with 
respect to their energy shell. We use variational theory to prove 
that, under global hypothesis, many of these oscillations 
have an homoclinic orbit, more precisely we prove that the periodic 
orbits having an homoclinic are dense in the invariant plane 
outside of a compact set. The major difficulty here is that the 
periodic orbits are not hyperbolic with repect to the full phase space.