15-106 Xiaolong He, Rafael de la Llave

Construction of Quasi-periodic Solutions of State-dependent Delay Differential Equations by the Parameterization Method II: Analytic case (330K, PDF) Nov 9, 15

Abstract , Paper (src), View paper (auto. generated pdf), Index of related papers

Abstract. We construct analytic quasi-periodic solutions of state-dependent delay differential equations with quasi-periodically forcing. We show that if we consider a family of problems that depends on one dimensional parameters(with some non-degeneracy conditions), there is a positive measure set $\Pi$ of parameters for which the system admits analytic quasi-periodic solutions. The main difficulty to be overcome is the appearance of small divisors and this is the reason why we need to exclude parameters. Our main result is proved by a Nash-Moser fast convergent method and is formulated in the a-posteriori format of numerical analysis. That is, given an approximate solution of a functional equation which satisfies some non-degeneracy conditions, we can find a true solution close to it. This is in sharp contrast with the finite regularity theory developed in

Files: 15-106.src( 15-106.keywords , analytic case.pdf.mm )