### Metastable states for weakly damped hamiltonian systems

Jean-Pierre Eckmann

Abstract.
(Joint work with C. Eugene Wayne)
Metastable motions are believed to inhibit the transport of energy
through Hamiltonian, or nearly Hamiltonian, systems with
many degrees of freedom. We investigate this question in a very
simple model (discrete nonlinear Schroedinger equation)
in which the breather solutions that are responsible for
the metastable states can be computed perturbatively to an arbitrary order.
Then, using a modulation hypothesis, we derive estimates for the rate
at which the system drifts along a manifold of periodic orbits and
verify the optimality of our estimates numerically.