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V. I. Arnold. Critical points of functions on a manifold with boundary, the simple lie groups Bk,Ck and F4 and singularities of evolutes. Russian Mathematical Surveys, 1978, 33(5): 99-116.

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• 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.