含两组状态变量且参数具有对称性的等变分歧问题及其开折的稳定性

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基金项目: 国家自然科学基金资助项目(10671002);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)

Stability of Equivariant Bifurcation Problems With Two Types of State Variables and Their Unfoldings in the Presence of Parameter Symmetry

School of Mathematical Science and Computing Technology, Central South University, Changsha 410083, P. R. China;
College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, P. R. China

摘要: 基于奇点理论中光滑映射芽的接触等价关系，讨论含两组状态变量且分歧参数带有对称性的等变分歧问题及其开折的稳定性，得到了一些基本结果，并且用横截性条件刻划了等变分歧问题的稳定性．
- 等变分歧问题 /
- 开折 /
- 稳定 /
- 无穷小稳定
Abstract: Based on the contact equivalent relation of smooth map-germs in singularity theory,the stability of equivariant bifurcation problems with two types of state variables and their unfoldings in the presence of parameters symmetry was discussed.Some basic results are obtained.Transversality condition was used to characterize the stability of equivariant bifurcation problems.
- equivariant bifurcation problem /
- unfolding /
- stability /
- infinitesimal stability

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