理论数学

Vol.2 No.2 (April 2012)

光滑函数的退化临界点的识别
The Recognition of Degenerate Critical Points of Smooth Functions

 

作者:

王伟 , 李养成

 

关键词:

识别问题内蕴理想高阶项Recognition Problems Intrinsic Ideals Higher-Order Terms

 

摘要:

本文应用分歧理论所发展的一些方法与技巧,研究位于子流形上的光滑函数的退化临界点的识别问题,建立了RH -等价理论,包括两函数芽RH -等价的判别定理,识别问题高阶项的精确表达形式及低阶项的刻画等。

By some methods and techniques developed from bifurcation theory, this paper investigates the recognition problem of degenerate critical points of smooth functions. Each one of such critical points lies on a sub-manifold included in domain of function. The so-called RH -equivalence theory is established, including a theorem to insureRH -equivalence between two function-germs, an exact formula for higher-order terms, a characterization of low-order terms, and so on.

文章引用:

王伟 , 李养成 (2012) 光滑函数的退化临界点的识别。 理论数学, 2, 53-61. doi: 10.12677/pm.2012.22010

 

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