= Liénard boundedness function
{c}
{title2=$W=V(x)+z^2/2-xz$}
For the Liénard system $\dot x=z-F(x)$, $\dot z=-g(x)$ with $F=x^3/3-2x$, $g=x^3-x$, and $V'=g$, the displayed function is coercive up to a constant. Differentiation gives $\dot W=-gF-z^2+Fz+xg\leq-z^2/2-5x^6/18+8x^4/3-x^2$. Its <derivative> is negative outside a <compact set>, providing bounded forward dynamics even though the original oscillator has negative damping near the origin. The coordinate $z=y+F(x)$ exposes this restoring and damping balance.
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