| 分歧参数带有对称性等变分歧问题及其开折的稳定性 |
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| 引用本文： | 郭瑞芝,任耀庆,万勇,唐钊轶.分歧参数带有对称性等变分歧问题及其开折的稳定性[J].长沙交通学院学报,2008,24(4):93-101. |
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| 作者姓名： | 郭瑞芝 任耀庆 万勇 唐钊轶 |
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| 作者单位： | 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 |
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| 基金项目： | 湖南省自然科学基金资助项目
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湖南省教育厅资助项目
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| 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．
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| 关 键 词： | 等变分歧问题 开折 稳定性 |
The stability of equivariant bifurcation problems with parameters symmetry and their unfoldings |
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| GUO Rui-zhi,REN Yao-qing,WAN Yong,TANG Zhao-yi.The stability of equivariant bifurcation problems with parameters symmetry and their unfoldings[J].Journal of Changsha Communications University,2008,24(4):93-101. |
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| Authors: | GUO Rui-zhi REN Yao-qing WAN Yong TANG Zhao-yi |
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| Institution: | GUO Rui-zhi1,REN Yao-qing1,WAN Yong2,TANG Zhao-yi1(1.College of Mathematics , Computer Science,Hunan Normal University,Changsha 410081,China,2.College of Mathematics , Computing Science,Changsha University ofScience & Technology,Changsha 410076,China) |
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| Abstract: | 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. |
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| Keywords: | equivariant bifurcation problem unfolding stability |
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