Hek Geertje
Universiteit van Amsterdam, Amsterdam, The Netherlands.
J Math Biol. 2010 Mar;60(3):347-86. doi: 10.1007/s00285-009-0266-7. Epub 2009 Apr 5.
Geometric singular perturbation theory is a useful tool in the analysis of problems with a clear separation in time scales. It uses invariant manifolds in phase space in order to understand the global structure of the phase space or to construct orbits with desired properties. This paper explains and explores geometric singular perturbation theory and its use in (biological) practice. The three main theorems due to Fenichel are the fundamental tools in the analysis, so the strategy is to state these theorems and explain their significance and applications. The theory is illustrated by many examples.
几何奇异摄动理论是分析时间尺度上有明显分离问题的有用工具。它利用相空间中的不变流形来理解相空间的全局结构或构造具有所需性质的轨道。本文解释并探讨了几何奇异摄动理论及其在（生物）实践中的应用。由费尼切尔提出的三个主要定理是分析中的基本工具，因此策略是陈述这些定理并解释它们的意义和应用。文中通过许多例子对该理论进行了说明。
