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Quasi-periodic breathers in Hamiltonian networks of long-range coupling. (English) Zbl 1153.37434

Summary: 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.

MSC:

37K60 Lattice dynamics; integrable lattice equations
37K55 Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems
05C45 Eulerian and Hamiltonian graphs
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