 15105 Xiaolong He, Rafael de la Llave
 Construction of Quasiperiodic Solutions
of Statedependent Delay Differential
Equations by the Parameterization Method I: finitely differentiable, hyperbolic case
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Nov 9, 15

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Abstract. In this paper, we use the parameterization method
to construct
quasiperiodic solutions of statedependent delay differential equations.
For example
$$
\left\{
egin{aligned}
\dot{x}(t)&=f( heta,x(t),\epsilon x(t au(x(t))))\
\dot heta(t)&=\omega.
\end{aligned}
ight.
$$
Under the assumption of exponential dichotomies
for the $\epsilon=0$ case, we use a contraction
mapping argument to prove the existence and smoothness of the
quasiperiodic solution. Furthermore, the result is given in an
$aposteriori$ format. The method is very general and applies also
to equations with several delays, distributed delays etc.
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