Stability of discrete breathers

We approach the problem of linear stability of discrete breathers in a rigorous way for networks of not necessarily identical oscillators with general type of coupling. In the case of Hamiltonian systems, using symplectic signature theory we give general conditions on the spectrum of the monodromy map in the uncoupled limit such that the discrete breathers are l(2)-linearly stable for weak enough coupling. We consider also dissipative networks of oscillators. In this case we prove that the discrete breathers are not only stable but also attract a neighbourhood of initial data for any choice of l(p)-topology. Some examples are considered amongst which an instance of "roto-breather". (C) 1998 Elsevier Science B.V.