Construction of quasi-periodic solutions of delay differential equations via KAM techniques

This work focuses on the existence of quasi-periodic solutions for linear autonomous delay differential equation under quasi-periodic time-dependent perturbation near an elliptic–hyperbolic equilibrium point. Using the time-1 map of the solution operator, Newton iteration scheme, space splitting and KAM techniques, it is shown that under appropriate hypothesis, there exist quasi-periodic solutions with the same frequencies as the perturbation for most parameters. We show that if the delay differential equation is analytic, we obtain analytic parameterizations of the solutions.