An Algebraic Criterion for Symmetric Hopf Bifurcation
Proc. R. Soc. London. 440 (1993) 727-732
In this paper we show that there is a group-theoretic restriction on the subgroup of symmetries in order for that subgroup to have a two-dimensional fixed-point subspace in any representation. This group-theoretic restriction is in many cases computable and substantially simplifies the calculations needed to find solutions supported on two-dimensional fixed-point subspaces. We illustrate this assertion by determining all of the periodic solutions supported on two-dimensional fixed-point subspaces for all of the (l even) irreducible representations of SO(3).