等变两参数分歧问题开折的惟一性和稳定条件

The uniqueness and stability conditions of unfoldings of equivariant two-parameter bifurcation problems

在U -等价群作用的情形下 ,用奇点理论方法对含有两个向量值参数的等变分歧问题的开折进行研究 .得出了在一定的条件下 ,分歧问题的U -等价轨道与其通用开折的等价类是一一对应的结论 ,并给出了分歧问题余维有限开折稳定的充分必要条件 .

Under the action of U -equivalent group, the unfoldings of equivariant two-(vector-valued) parameter bifurcation problems are studied by the methods in singularity thoery. The main results:(1) the equivalence classes of versal unfoldings of bifurcation problems are one-to-one corresponding to the orbits of the bifurcation problem; (2) the necessary and sufficient condition of stability of bifurcation problems.