Origin Preserving Path Formulation for Multiparameter Z₂-Equivariant Corank 2 Bifurcation Problems

Abstract

A singularity theory, in the form of path formulation, is developed to analyze and organize the qualitative behavior of multiparameter Z₂-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.