= Strong resonance of a planar map
{title2=$\lambda^k=1,\quad k\le4$}
= Strong resonances of a planar map
{synonym}
At a <strong resonance of a planar map> the <Floquet multiplier> of a <fixed point> is a root of unity of low order. The usual nonresonant <Neimark–Sacker bifurcation> requires $\lambda^k\ne1$ for $k=1,2,3,4$. At a 1:3 resonance a quadratic term $\overline z^2$ cannot be removed from the <normal form>; at a 1:4 resonance a cubic term $\overline z^3$ remains. Consequently one cannot infer a quasiperiodic invariant curve from the unit-modulus crossing alone.
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