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

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.