 15106 Xiaolong He, Rafael de la Llave
 Construction of Quasiperiodic Solutions of Statedependent Delay Differential Equations by the Parameterization Method II: Analytic case
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Nov 9, 15

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Abstract. We construct analytic quasiperiodic solutions of statedependent delay differential equations with
quasiperiodically forcing. We show that if we consider a family of problems that depends on
one dimensional
parameters(with some nondegeneracy conditions), there is a positive measure set $\Pi$
of parameters for which the system
admits analytic quasiperiodic 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 NashMoser fast convergent method and is formulated in the aposteriori
format of numerical analysis. That is, given an approximate solution of a functional equation which satisfies some
nondegeneracy conditions, we can find a true solution close to it.
This is in sharp contrast with the finite regularity theory developed in
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