Quasi-periodic breathers in Hamiltonian networks of long-range coupling

This work is concerned with Hamiltonian networks of weakly and long-range coupled oscillators with either variable or constant on-site frequencies. We derive an infinite dimensional KAM-like theorem by which we establish that, given any N -sites of the lattice, there is a positive measure set of small amplitude, quasi-periodic breathers (solutions of the Hamiltonian network that are quasi-periodic in time and exponentially localized in space) having N -frequencies which are only slightly deformed from the on-site frequencies.