分歧参数带有对称性的等变分歧问题在左右等价群下的开折

Unfoldings of Equivariant Bifurcation Problems with Parameter Symmetry under a Left-Right Equivalent Group

利用奇点理论中光滑映射芽的左右等价理论,引进状态变量和分歧参数均具有对称性且它们的对称性可以不同的等变分歧问题,讨论这种等变分歧问题关于左右等价群的开折,得到这种多参数等变分歧问题的一开折为通用开折的充要条件.

Based on the theory of left-right equivalence of smooth map germs in sigularity theory, multiparameter equivariant bifurcation problems of state varibles with symmetry and parameters with symmetry were introduced. The unfoldings of such equivariant bifurcation problems with respect to left-right equivalence were discussed. The necessary and sufficient conditions for an unfolding of such a multiparameter equivariant bifurcation problem to he versal were obtained.