On the Iterates of Digit Maps

Zachary Chase

Given a base $b$, a "digit map" is a map $f:{\mathbb{Z}}^{\ge 0}\to {\mathbb{Z}}^{\ge 0}$ of the form $f({\sum }_{i=0}^n{a}_i{b}^i)={\sum }_{i=0}^n{f}_{\ast }(a_i)$, $0\le a_i\le b-1$ for each $…