E. Ihrig and M. Golubitsky

Pattern selection with O(3) symmetry

Physica. 13D (1984) 1-33.

• Abstract

For each irreducible representation of S0(3) and 0(3) we determine, up to conjugacy, all isotropy subgroups and identify, in particular, the maximal isotropy subgroups. Each isotropy subgroup corresponds to a possible planform for the spherical Benard problem. Using an equivariant branching lemma of Cicogna we prove, for each of these representations, the existence of solutions corresponding to a number of different planforms, thus extending substantially the work of Busse and Sattinger. We also give a useful criterion for showing when solutions obtained by the equivariant branching lemma must be unstable.