Iterating sine, equivalence classes of variable changes, and groups with few conjugacy classes

Pavel Etingof

This is an expository paper about iterations of a smooth real function $f$ on $[0,\epsilon )$ such that $f(0)=0$, $f^{\prime }(0)=1$, and $f(x)<x$ for $x>0$, i.e., the sequence defined by…