= Stable-variable lag in nilpotent center-manifold reduction
For $\dot z=v/2$, $\dot v=-3v/2+3w$, $\dot w=-(z-v)^3/9$, the stable coordinate is $v-2w$ and the <center manifold> begins with $v=2w$. A cubic correction $h_3$ satisfies $w\partial_z h_3-(2/9)(z-2w)^3=-3h_3/2$, giving $h_3=4z^3/27-32z^2w/27+272zw^2/81-832w^3/243$. The derivative of the graph contributes at the same order as the cubic forcing. Simply setting $\dot v=0$ omits this lag and incorrectly changes the cubic damping coefficient of the reduced <normal form>.
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