含两组状态变量的等变分歧问题在左右等价群下的开折  

Unfolding of Multiparameter Equivariant Bifurcation Problems With Two Groups of State Variables Under Left-Right Equivalent Group

作　　者：郭瑞芝[1] 李养成[1] 

机构地区：[1]中南大学数学科学与计算技术学院

出　　处：《应用数学和力学》2005年第4期489-496,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10271023);湖南省自然科学基金资助项目(04JJ3072);湖南省教育厅基金资助项目(04C383)

摘　　要：　基于奇点理论中光滑映射芽的左右等价关系,讨论多参数等变分歧问题关于左右等价的开折·　将这种等变分歧问题的状态变量分为两组,其中属于同一组的诸状态变量可以独立地变化,而属于另一组的诸状态变量在变化过程中依赖于前一组中的诸状态变量·　应用光滑映射芽开折理论中的相关方法和技巧。Based on the left_right equivalent relation of smooth map_germs in singularity theory, the unfoldings of multiparameter equivariant bifurcation problems with respect to left_right equivalence are discussed. The state variables of such an equivariant bifurcation problem were divided into two groups, in which the first can vary independently, while the others depend on the first in the varying process. By applying related methods and techniques in the unfolding theory of smooth map_germs, the necessary and sufficient condition for an unfolding of a multiparameter equivariant bifurcation problem with two groups of state variables to be versal is obtained.

关 键 词：等变分歧问题 左右等价群 开折 

分 类 号：O189.3[理学—数学] O177.91[理学—基础数学]