Response solutions of 2-dimensional degenerate systems under quasi-periodic perturbations

This paper considers quasi-periodic perturbations of 2-dimensional degenerate systems. It is proved that if the equilibrium point of the unperturbed system is hyperbolic-type degenerate, then the perturbed sys-tem has a small response solution. The proof is based on the topological degree theory and some KAM techniques developed in [3]. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates quasi-periodic perturbations of 2-dimensional degenerate systems. It is demonstrated that if the equilibrium point of the unperturbed system is hyperbolic-type degenerate, then the perturbed system has a small response solution. The proof relies on the topological degree theory and some KAM techniques developed in [3].