Cusp points and pitchfork interactions in equivariant bifurcation problems (Q688870)

The relation between the concept of a cusp point for a mapping between Banach spaces and the interaction of two classical pitchfork bifurcations in equivariant spaces is considered. 2 parameter problems are considered by an approach based on linear normal form theory, Lyapunov-Schmidt reduction and restriction to solutions with appropriate isotropies. Results are applied to some boundary value problems.