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We prove that there is an invariant torus with given Diophantine frequencyvector for a class of Hamiltonian systems defined by an integrable largeHamiltonian function with a large non-autonomous Hamiltonian perturbation. Asfor application, we prove that a finite network of Duffing oscillators withperiodic exterior forces possesses Lagrangian stability for almost all initialdata.

KAM theorem with large perturbation and application to network of Duffing oscillators