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设En是在0∈Rn的C∞函数芽环,M是En中唯一的极大理想.如果f∈M2且其二阶Hessain是非退化的,则f同构于它的二阶Hessain,这就是著名的Morse引理.本文将讨论两个变元的C∞函数芽,得到:(1)若f∈M3?Exy,且其三阶Hessain是非退化的,则f同构于它的三阶Hessain.(2)若f∈M4?Exy 相似文献
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光滑映射芽的有限决定性是奇点理论中一个重要专题 .对函数芽的有限决定性问题 ,主要是在右等价群及其一些子群作用下来讨论的 .本文在 [1]和 [4 ]的基础上讨论函数芽在右等价群的正规子群 R*n (S;n)作用下的有限决定性 ,并组出函数芽有限 R*r (S;n) -决定的一个充分必要条件 . 相似文献
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We show that the bi-Lipschitz equivalence of analytic function germs (2, 0)(, 0) admits continuous moduli. More precisely, we propose an invariant of the bi-Lipschitz equivalence of such germs that varies continuously in many analytic families f
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: (2, 0)(, 0). For a single germ f the invariant of f is given in terms of the leading coefficients of the asymptotic expansions of f along the branches of generic polar curve of f. 相似文献
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TOSHIZUMI FUKUI 《Compositio Mathematica》1997,105(1):95-108
We introduce some blow-analytic invariants of real analytic function-germsand discuss their properties. As a consequence, we obtain, for instance, the multiplicity of function-germs is a blow-analytic invariant. 相似文献
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本文用一个十分简单的例子说明[1]对整体的Borel定理的证明是错误的.为此, 还须介绍函数芽和函数芽序列一致收敛的概念,并给出一个判定引理. 相似文献
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In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations. 相似文献
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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=x2y+∑i=4kpi(x,y),f2=xy2+∑i=4kqi(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. 相似文献
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Xu XU 《数学学报(英文版)》2007,23(4):711-714
Risler & Trotman in 1997 proved that the multiplicity of an analytic function germ is left-right lipschitz invariant, which provided a partial answer to Zariski conjecture. In this note, based on the recent work of Comte, Milman & Trotman, we generalize the work of them to prove that the multiplicity of a C^∞ differentiable function germ is also left-right lipschitz invariant. 相似文献
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