= Hopf coordinates for two real representation copies
{c}
{title2=$(q_1,q_2)=(z_1,\bar z_2)$}
Spatially complex coordinates on two real copies need not both have the same temporal phase weight. If their time-circle action is $(z_1,z_2)\mapsto(e^{-i\phi}z_1,e^{i\phi}z_2)$, conjugating the second coordinate gives a common Hopf phase. The linear terms then have the same imaginary frequency in $q$ coordinates but opposite imaginary frequencies in the original $z$ coordinates. Failing to make this conjugation produces amplitude equations inconsistent with the specified symmetries.
// Target: dynamical-systems.bigb
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