Response Solutions of Degenerate Quasi-Periodic Systems Under Small Perturbations

This paper considers a class of n-dimensional degenerate systems with a quasi-periodic perturbation whose frequency is a diophantine vector. Assume that the unperturbed system has the origin as an equilibrium, which is degenerate at one direction. By KAM iteration, we prove that the perturbed quasi-periodic system has a small response solution for sufficiently small perturbations. The proof is based on the idea of reducibility and the KAM technique of introducing parameters.