摘要：
本文主要研究二元C∞ 函数芽环中函数芽的性质问题.利用Mather有限决定性定理和C∞ 函数的右等价关系,获得了带有任意4次至k次齐次多项式pi(x,y),qi(x,y)(i=4,5,· · ·,k)的两类函数芽f1=x2 y+(k∑i=4)pi(x,y),f2=xy2+(k∑i=4)qi(x,y)(k≥5)的一个共同性质:若Mk2?M2J(fj)(j=1,2)且f1,f2的轨道切空间的余维分布均为ci=1(i=4,5,· · ·,k?1),则对这里的i,pi(x,y)中xyi?1,yi的系数和qi(x,y)中xi?1y,xi的系数均为零.最后,利用该性质,给出了f1,f2和一类余维数为7的二元函数芽的标准形式.%In this paper, we mainly consider a property of function germs in the ring of C∞ functions germs of two variables. Using the Mather's theorem of finite determinacy and right equivalence of functions, a common property of two types of function germs f1=x2y+(k ∑ i=4)pi(x,y) and f2 = xy2 + (k ∑ i=4) qi(x, y)(k ≥ 5) with some arbitrary homogeneous polynomials pi(x, y) and qi(x, y)(i = 4, 5, · · · , k) of degree from 4 to k is obtained. If Mk2 ? M2J(fj)(j = 1, 2) and the codimension distribution of tangent space of orbits for f1, f2 are both ci = 1(i = 4, 5, · · · , k?1), the coefficients of xyi?1 and yi in pi(x, y) are both zero, so are the coefficients of xi?1y and xi in qi(x, y) . Finally, by this property, the normal forms of f1, f2 and a class of function germs of two variables with codimension 7 are given.
