Extending geometric singular perturbation theory to nonhyperbolic points - Fold and canard points in two dimensions
Extending geometric singular perturbation theory to nonhyperbolic points - Fold and canard points in two dimensions
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DOI：
10.1137/s0036141099360919
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发表时间：
2001-09-07
影响因子：
2
通讯作者：
Szmolyan, P
中科院分区：
文献类型：
--
作者：
Krupa, M;Szmolyan, P
奇异摄动问题的几何方法是基于动力系统理论的强大方法。这些技术在正常双曲临界流形的情况下已经非常成功。然而，在正常的双曲失败的点，发达的几何理论不适用。我们提出了一种基于爆破技术的方法，从而导致这些问题的严格的几何分析。详细分析了平面系统中慢流形过折叠点和鸭点的扩张。强调了各种图表的有效使用。
The geometric approach to singular perturbation problems is based on powerful methods from dynamical systems theory. These techniques have been very successful in the case of normally hyperbolic critical manifolds. However, at points where normal hyperbolicity fails, the well-developed geometric theory does not apply. We present a method based on blow-up techniques, which leads to a rigorous geometric analysis of these problems. A detailed analysis of the extension of slow manifolds past fold points and canard points in planar systems is given. The efficient use of various charts is emphasized.