= Superstable periodic orbit
= Super-stable periodic orbit
{synonym}
A <periodic orbit> of a differentiable <interval map> is superstable when its <periodic-orbit multiplier> vanishes. A cycle passing through a <critical point> has zero multiplier because the <derivative> product includes $f'(c)=0$. For the nonconstant quadratic family $f_\mu(x)=1-\mu x^2$, a superstable $2^n$ cycle satisfies $f_\mu^{2^n}(0)=0$ and does not have a smaller critical period.
// Target: dynamical-systems.bigb
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