We study metastable motions in weakly damped Hamiltonian systems. These 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 in which the breather solutions that are thought to be 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 this manifold of periodic orbits and verify the optimality of our estimates numerically.
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Figure 1.
Numerical illustration of the dynamics with (weak) dissipation. The parameters are
Figure 2.
The cylinder illustrates the set of periodic solutions of Eq.(9), with
Figure 3.
The figure shows the
Figure 4.
This graph illustrates the behavior of
Figure 5.
This graph illustrates the decay properties of the
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