Abstract. 
I will consider a Hamiltonian system describing a pendulum weakly coupled
with an arbitrary number of anharmonic oscillators. A large proportion of
the phase space is filled by invariant tori supporting regular motion with
bounded trajectories and action variables close to those in the uncoupled
case.

It is well known that transversal intersections of the unstable manifolds
with stable manifolds of such tori not only induce chaos but can result in
global instability through drift of actions. One is lead to study the
intersection "angle" between the manifolds. I will explain why the latter
is (at most) exponentially small with respect to the forcing rapidity.