Z_2对称奇点理论的若干命题和定理

Several Propositions and Theorems in Singularity Theory with Z_2-Symmetry

本文指出由Golubitsky和Schaeffer给出的恒等关系Itr(F,Z_2)=(ItrF)·{x}是错误的。在此给出了Z_2对称奇点理论的若干结论,重新证明了Golubitsky和Langford关于规范形的两个重要定理。借助同样的思想,可以重新给出非对称情形下相应规范形定理的证明,以弥补原证明中的漏洞。

This paper points out that the identity Itr(F,Z_2)=(ItrF)·{x}given by Golubitsky andSchaeffer is not correct. Several results of singularity theory with Z_2-symmetry are givenhere,two important theorems about normal forms, given by Golubisby and Langford,are reproved here, From the same ideals, We can rewrite the proofs of the interrelatednormal form theorems in the unsymmetric context.