A KAM Theorem with Large Twist and Finite Smooth Large Perturbation

• Lu Chen ^[1]
  1. [1] Quzhou University

     Quzhou University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 3, 2023
• Idioma: inglés
• Enlaces
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• Resumen

  • We study non-degenerate Hamiltonian systems of the form H(θ , t, I) = H0(I) εa + P(θ , t, I) εb , where (θ , t, I) ∈ Td+1× [1, 2] d (T := R/2πZ), a, b are given positive constants with a > b, H0 : [1, 2] d → R is real analytic and P : Td+1 × [1, 2] d → R is C with = 2(d+1)(5a−b+2ad) a−b + μ, 0 < μ 1. We prove that, for the above Hamiltonian system, if ε 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.

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