= Trace formula for periodic points of a subshift
{title2=$\#\operatorname{Fix}(\sigma^n)=\operatorname{tr}(A^n)$}
A <fixed point> of the $n$th <iteration of a map> of a <subshift of finite type> is determined uniquely by its length-$n$ block with a permitted closing transition. Summing the counts of length-$n$ closed walks over their starting symbols gives the displayed <trace>. This counts points whose least period divides $n$. If $P_n$ counts points of least period exactly $n$, then $\operatorname{tr}(A^n)=\sum_{d\mid n}P_d$, and <Möbius inversion> gives $P_n=\sum_{d\mid n}\mu_{\mathrm M}(n/d)\operatorname{tr}(A^d)$. The number of distinct least-period-$n$ <periodic orbits> is $P_n/n$.
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