Unfolding of Multiparameter Equivariant Bifurcation Problems With Two Groups of State Variables Under Left-Right Equivalent Group
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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,得到了一个含两组状态变量的多参数等变分歧问题的开折是通用开折的充要条件.Abstract: 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.
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Key words:
- equivariant bifurcation /
- left-right equivalent group /
- unfolding
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