Construction of Quasi-periodic Solutions of State-Dependent Delay Differential Equations by the Parameterization Method I: Finitely Differentiable, Hyperbolic Case

摘要

In this paper, we use the parameterization method to construct quasi-periodic solutions of state-dependent delay differential equations. For example Under the assumption of exponential dichotomies for the case, we use a contraction mapping argument to prove the existence and smoothness of the quasi-periodic solution. Furthermore, the result is given in an a posteriori format. The method is very general and applies also to equations with several delays, distributed delays etc.