Integer Dynamics

Let $b \geq 2$ be an integer, and write the base $b$ expansion of any non-negative integer $n$ as $n=x_0+x_1b+\dots+ x_{d}b^{d}$, with $x_d>0$ and $ 0 \leq x_i < b$ for $i=0,\dots,d$. Let $ϕ(x)$ denote an integer polynomial such that $ϕ(n) >0$ for all $n>0$. Consider the map $S_{ϕ,b}: {\mathbb Z}_{\... View More