KAM theorem with large twist and finite smooth large perturbation

Abstract

In the present paper, we will discuss the following non-degenerate Hamiltonian systemWe prove that if ε is sufficiently small, there is an invariant torus with given Diophantine frequency vector for the above Hamiltonian system. As for application, we prove that a finite network of Duffing oscillators with periodic exterior forces possesses Lagrangian stability for almost all initial data.