We characterize the existence of an exponential dichotomy for a nonautonomous linear delay equation via the hyperbolicity of an appropriate cocycle. An important advantage of this approach is that the base is compact under mild additional assumptions. Moreover, we give a few applications of the equivalence of the two notions of hyperbolicity. In particular, we consider the robustness and the admissibility of the equation, and we obtain stable and unstable invariant manifolds.

中文翻译：

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通过cocycles延迟方程的双曲性

我们通过适当的共循环的双曲性来表征非自治线性延迟方程的指数二分法的存在。这种方法的一个重要优点是在温和的附加假设下基是紧凑的。此外，我们给出了两个双曲线概念的等价性的一些应用。特别地，我们考虑了方程的鲁棒性和可接受性，我们得到了稳定和不稳定的不变流形。