KAM tori for two dimensional completely resonant derivative beam system

Abstract

In this paper, we introduce an abstract KAM (Kolmogorov–Arnold–Moser) theorem. As an application, we study the two-dimensional completely resonant beam system under periodic boundary conditions. Using the KAM theorem together with partial Birkhoff normal form method, we obtain a family of Whitney smooth small–amplitude quasi–periodic solutions for the equation system.