分歧参数带有对称性等变分歧问题及其开折的稳定性  

The stability of equivariant bifurcation problems with parameters symmetry and their unfoldings

作　　者：郭瑞芝[1] 任耀庆[1] 万勇[2] 唐钊轶[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 [2]长沙理工大学数学与计算科学学院,湖南长沙410076

出　　处：《长沙交通学院学报》2008年第4期93-101,共9页Journal of Changsha Communications University

基　　金：湖南省自然科学基金资助项目(07JJ6008);湖南省教育厅资助项目(05C267;08C578)

摘　　要：借助光滑映射奇点理论中的接触等价,定义分歧参数带有对称性的等变分歧问题及其开折,研究这种分歧问题的稳定性.得到的这种分歧问题的无穷小稳定与稳定是等价的,而且讨论了这种分歧问题开折的稳定性,得到了一定条件下分歧问题开折稳定的充分必要条件为该开折是通用开折.The equivariant bifurcation problems with parameters symmetry and their unfoldings are defined via contacting equivalence in singularity theoretically. The stability of such kind of equivariant bifurcation problems is studied. The equivalence of infinite singal stability is obtained. Moreover, the stability of unfoldings of such kind of bifurcation problems is discussed, and the sufficient condition of an unfolding of a bifurcation problem to be stable is that it is versal unfolding under certain conditions.

关 键 词：等变分歧问题 开折 稳定性 

分 类 号：O192[理学—数学]