A singularity theory, in the form of path formulation, is developed to analyze and organize the qualitative behavior of multiparameter [Formula: see text]-equivariant bifurcation problems of corank 2 and their deformations when the trivial solution is preserved as parameters vary. Path formulation allows for an efficient discussion of different parameter structures with a minimal modification of the algebra between cases. We give a partial classification of one-parameter problems. With a couple of parameter hierarchies, we show that the generic bifurcation problems are 2-determined and of topological codimension-0. We also show that the preservation of the trivial solutions is an important hypotheses for multiparameter bifurcation problems. We apply our results to the bifurcation of a cylindrical panel under axial compression.

中文翻译：

---

多参数ℤ2-等变Corank 2分岔问题的原点保留路径公式

以路径公式的形式开发了一种奇点理论，用于分析和组织多参数 [公式：见文本]-等变分岔问题的 corank 2 及其变形，当参数变化时保留平凡解时它们的变形。路径公式允许对不同参数结构的有效讨论，只需对案例之间的代数进行最小修改。我们给出了单参数问题的部分分类。通过几个参数层次结构，我们证明了通用分岔问题是 2-determined 和拓扑 codimension-0。我们还表明，保留平凡解是多参数分岔问题的一个重要假设。我们将我们的结果应用于轴向压缩下圆柱形面板的分叉。