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

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 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.

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