标题:
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
关键字:
识别问题, 内蕴理想, 高阶项Recognition Problems; Intrinsic Ideals; Higher-Order Terms
期刊名称:
《Pure Mathematics》, Vol.2 No.2, 2012-04-26
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.