= First-order canonical removal of a cubic oscillator perturbation
{title2=$x=X-\lambda X^2/(m\omega^2)-2\lambda P^2/(m^3\omega^4)$}
The accompanying <momentum> map is $p=P+2\lambda XP/(m\omega^2)$. Its <Poisson bracket> is one up to second-order corrections. Substitution into $p^2/(2m)+m\omega^2x^2/2+\lambda x^3$ cancels all terms linear in $\lambda$, leaving a harmonic <Hamiltonian> to that order. The map is local and perturbative, not an exact global removal of an unbounded cubic potential.
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