Axial subgroup

For a steady-state equivariant dynamical system, an axial subgroup has a one-dimensional real fixed-point subspace of a group action. A complex axial subgroup for a Hopf problem has a one-dimensional complex fixed-point subspace under the spatial group combined with the common phase action. Distinct conjugacy classes may yield distinct types of bifurcating branches.

For the spatial group combined with the temporal phase circle in an equivariant Hopf problem, a complex axial isotropy subgroup is an actual stabilizer whose fixed-point space is one complex line. Its real dimension is two. One must include the kernel of the combined action when writing the full stabilizer, not just a generator having the right fixed space.

// Target: dynamical-systems.bigb