带广义对称性的等变分歧问题的研究  

Discussion and Research of Equivariant Bifurcation Problem with Generalized Symmetry

作　　者：刘瑞娟[1] 施恩伟[1] 

机构地区：[1]云南师范大学数学学院,昆明650092

出　　处：《四川理工学院学报（自然科学版）》2009年第5期18-22,共5页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：云南省教育厅基金资助项目(07c11666)

摘　　要：文章将主要研究在广义对称条件下分歧问题的相关性质,提出ΓΔ-等变概念,它是一般定义下等变概念的推广,在此基础上研究在接触等价条件下ΓΔ-等变分歧问题的相关基本性质:ΓΔ-不变函数芽环上的有限生成模与相应切空间的性质,ΓΔ-等变分歧问题的开折是通用开折的一个充分必要条件。推广了前人工作的结果。In this paper, some main properties of bifurcation problem with generalized symmetry are studied. The main result is that the conception of ΓΔ - equivariance is given. It is an extension of general conception of ΓΔ - equivariance. On this base, some properties of ΓΔ - equivariant bifurcation problem under contact equivalence are obtained：the finite modules over the tings of ΓΔ - invariant functons and the property of its tangent space are obtained and an sufficient and necessary conditon that an unfolding of ΓΔ - bifurcation problem is a versal unfolding is given. Therefore, the results of predecessors are extended.

关 键 词：ΓΔ-等变分歧问题 通用开折 接触等价 

分 类 号：O189.3[理学—数学] O177.91[理学—基础数学]