= Pointwise periodic self-map
{title2=$\forall x\ \exists n_x\geq1:\ f^{n_x}(x)=x$}
A pointwise periodic self-map returns each point to itself after a positive number of iterates which may depend on the point. It is a <bijection>: each finite cycle supplies predecessors; equality of two images can be undone by an iterate with an exponent one below a common multiple of the two periods. The <set> consequently decomposes into disjoint finite <permutation cycles>. Pointwise periodicity does not imply that one iterate is the identity on an infinite <set>.
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