= Dihedral steady-state normal form
{title2=$\dot z=\mu z+a z|z|^2+b\bar z^{n-1}+\cdots$}
For the natural plane action of the <dihedral group>, rotations constrain monomial weights and reflection makes coefficients real. The reflection axes support the bifurcating equilibria. For $n=3$, the quadratic anisotropic term gives three transcritical-like branches that are saddles in the full plane. For $n=4$, cubic isotropic and anisotropic terms determine two reflection-isotropy classes. For $n=5$, the cubic isotropic term sets the leading radial amplitude while quartic anisotropy separates stable and saddle angular classes.
// Target: dynamical-systems.bigb
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