Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyse the future asymptotics of models which exhibit oscillatory behaviour, we provide a theorem concerning the large-time behaviour for solutions of a general class of systems. We thus propose our result to be applicable to a wide range of problems in spatially homogenous cosmology with oscillatory behaviour. Mathematically the theorem builds up on the standard theory of averaging in non-linear dynamical systems.

中文翻译：

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使用与时间相关的扰动参数求平均值

受数学宇宙学中最近问题的启发，其中应用时间平均方法来分析表现出振荡行为的模型的未来渐近性，我们提供了一个关于一般类系统解的大时间行为的定理。因此，我们建议我们的结果适用于具有振荡行为的空间同质宇宙学中的广泛问题。从数学上讲，该定理建立在非线性动力系统中平均的标准理论之上。