Quasi-periodic solutions for differential equations with an elliptic-type degenerate equilibrium point under small perturbations (Q2419927)

The paper studies the existence of quasi-periodic solutions to ordinary and delay differential equations (ODEs and DDEs, respectively) with an elliptic-type degenerate equilibrium point under quasi-periodic perturbations. The main results of the paper are stated in two theorems which provide sufficient conditions for the existence of quasi-periodic solutions to perturbed ODEs and DDEs near the equilibrium point for most parameter values. These results are then applied to the study of quasi-periodic solutions to the delayed van der Pol's oscillator with zero-Hopf singularity.