Solutions with subgroup symmetry for singular equations in bifurcation theory (Q875189)

On the base of previous results of the first author, general form of the branching equation, the subgroup structure for bifurcation problems admitting crystallographic group symmetries, is investigated. For dihedral symmetry, in particular for hexagonal symmetry \(D_6\), solutions invariant relative to subgroup structures for every chain of subgroups are constructed. Applications to nonlinearly perturbed Helmholtz equations are given. In the general case of finite group symmetry with known composition law, a computer program for the determination of all subgroups is given, in particular, for dihedral and also planar and spatial crystallographic groups.