Equivariant dynamical system
= Equivariant dynamical system
{title2=$F(gx,\mu)=gF(x,\mu)$}
An equivariant dynamical system has a <vector field> commuting with the action of a symmetry group. Its <flow map> preserves every subgroup's fixed-point subspace, because equivariance and uniqueness keep initial states fixed by that subgroup. Polynomial <normal forms> are constrained by the weights and parity of the <group representation>.