We describe all possible forms of the Sacker–Sell spectrum for a nonautonomous linear delay equation. In particular, the spectrum may have infinitely many connected components either accumulating at minus infinity or at a finite value. We also show that to each connected component of the spectrum one can associate a subspace of initial conditions whose lower and upper Lyapunov exponents are contained in the connected component. These spaces generate the whole ambient space. Finally, we give a condition under which the Lyapunov exponents of a nonlinear perturbation of a linear delay equation belong to a connected component of the spectrum.

中文翻译：

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延迟方程的谱

我们描述了一个非自治线性延迟方程的Sacker-Sell谱的所有可能形式。尤其是，频谱可能具有无限多个相连的分量，它们以负无穷大或有限值累加。我们还表明，可以将频谱的每个连通分量与一个初始条件的子空间相关联，该初始条件的上下Lyapunov指数包含在连通分量中。这些空间生成整个环境空间。最后，我们给出一个条件，在该条件下，线性延迟方程的非线性摄动的Lyapunov指数属于频谱的连接分量。