Iterative root

Summary

An iterative root of order $n$ of a map $f$ is a map $g$ whose $n$-th iterate is $f$, that is, $g \circ g \circ \cdots \circ g = f$ with $n$ factors. It is the analogue for composition of the $n$-th root of a number. Iterative roots may fail to exist, and when they exist there are often many of them. The search for them is one of the classical problems of iteration theory.