= Periodic point
{title2=$R^n(p)=p$}
A point $p$ is periodic for an iterated map $R$ if $R^n(p)=p$ for some positive integer $n$. Its exact period is the least such $n$, and the distinct points $p,R(p),\ldots,R^{n-1}(p)$ form its periodic orbit. For a holomorphic map its <periodic-orbit multiplier> is $(R^n)'(p)$, computed in a local coordinate; at infinity use a reciprocal coordinate. The chain rule makes this the cyclic product of derivatives along the orbit, so it is the same at every point of that orbit.
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