光滑函数的退化临界点的识别

The Recognition of Degenerate Critical Points of Smooth Functions

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R_H -等价理论，包括两函数芽R_H -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。

Abstract: 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 R_H -equivalence theory is established, including a theorem to insureR_H -equivalence between two function-germs, an exact formula for higher-order terms, a characterization of low-order terms, and so on.