不变函数芽的通用形变与有限决定性  

The versal deformation and finite determinacy of invariant function germs

作　　者：郭瑞芝[1] 陈达[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,湖南长沙410081

出　　处：《高校应用数学学报（A辑）》2013年第3期335-346,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10971060)

摘　　要：对函数芽引进对称性和相应的右等价群,探讨不变函数芽在该右等价群下的通用形变和有限决定性,定义了不变函数芽轨道切空间,切空间,和形变的形式切空间,不变函数芽形变的同构,通用形变等概念.证明了不变函数芽形变的平凡性引理,几何引理和代数引理,得到了不变函数芽的形变是通用形变的充分必要条件,分别给出了不变函数芽是有限决定的一个充分条件和一个必要条件.The symmetry of function germs and its corresponding right equivalent group are introduced.This paper discusses the versal deformation and finite determinacy of function germs under the right equivalent group,define concepts on the tangent space to an orbit,the tangent space of a function germs,the formal tangent space of a deformation,the isomorphism between two deformations of function germs,the versal deformation,and so on.The triviality lemma,the geometrical lemma and the algebraic lemma of invariant function germs are proved.A necessary and sufficient condition of a deformation of an invariant function germ to be versal is obtained.A necessary condition and a sufficient condition of an invariant function to be definitely determinated are given respectively.

关 键 词：不变函数芽 右等价群 通用形变 有限决定性 

分 类 号：O192[理学—数学]