Quasi periodic breathers in Hamiltonian lattices with symmetries

We prove existence of quasiperiodic breathers in Hamiltonian lattices of weakly coupled oscillators having some integrals of motion independent of the Hamiltonian. The proof is obtained by constructing quasiperiodic breathers in the anticontinuoum limit and using a recent theorem by N.N. Nekhoroshev [8] as extended in [5] to continue them to the coupled case. Applications to several models are given.