Geng, J; Viveros, J.; Yi, Y. Quasi-periodic breathers in Hamiltonian networks with long-range coupling. Physica D, vol. 237 (2008), pp. 2866-2892 doi:10.1016/j.physd.2008.05.010
This work is concerned with Hamiltonian networks of weakly and long-range coupled oscillators with either variable or constant on-sitefrequencies. We derive an infinite dimensional KAM-like theorem by which we establish that, given any N-sites of the lattice, there is a positivemeasure set of small amplitude, quasi-periodic breathers (solutions of the Hamiltonian network that are quasi-periodic in time and exponentiallylocalized in space) having N-frequencies which are only slightly deformed from the on-site frequencies.