A group-theoretic approach to computational bifurcation problems with symmetry (Q1118452)

The author presents a group-theoretic approach to the computation of global solution branches, limit points, and bifurcation points of parameter-dependent equations of the form (1) \(f(u,\lambda)={\mathbb{O}}\), where f: \({\mathbb{R}}^ n\times {\mathbb{R}}\to {\mathbb{R}}^ n\) is a smooth, vector-valued function possessing some equivariance properties, \(u\in {\mathbb{R}}^ n\) is the vector of the state variables, and \(\lambda\in {\mathbb{R}}\) is some parameter. The basic idea consists in reducing problem (1) on the basis of the equivariance properties observed. Afterwards the reduced problems can be analyzed by standard methods. The author impressively demonstrates the efficiency of his technique in analyzing a lattice-dome structure with hexagonal symmetry in detail.