= Near-identity transformation
{title2=$x=y+h(y),\quad Dh(0)=0$}
A near-identity transformation is a local <change of variables> whose derivative at the reference point is the identity. In a <normal form of a dynamical system>, substituting $x=y+h(y)$ and solving $(I+Dh(y))\dot y=f(y+h(y))$ determines which nonlinear coefficients can be removed. The transformation is locally invertible by the <inverse function theorem>. Terms whose removal equations are singular are resonant and must be retained; a computed zero resonant coefficient cannot be assigned an arbitrary nonzero value by normalization.
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