A KAM Theorem with Large Twist and Finite Smooth Large Perturbation

We study non-degenerate Hamiltonian systems of the form H(theta, t, I) = H-0(I)/epsilon(a) + P(theta, t, I)/epsilon(b), where (theta, t, I) is an element of Td+1 x [1, 2](d) (T := R/2 pi Z), a, b are given positive constants with a > b, H-0 : [1, 2](d) -> R is real analytic and P : Td+1 x [1, 2](d). R is C-l with l = 2(d+1)(5a-b+2ad)/a-b + mu, 0 < mu << 1. We prove that, for the above Hamiltonian system, if e is sufficiently small, there is an invariant torus with given Diophantine frequency vector which obeys conditions (1.7) and (1.8). As for application, a finite network of Duffing oscillators with periodic external forces possesses Lagrange stability for almost all initial data.

Automated summary

In this study, a class of non-degenerate Hamiltonian systems were investigated. It was proven that under certain conditions, for sufficiently small parameter e, there exists an invariant torus satisfying specific conditions. Additionally, it was found that a finite network of Duffing oscillators with periodic external forces exhibits Lagrange stability for almost all initial data.