The emergence of 4-cycles in polynomial maps over the extended integers

Andrew Best, Patrick Dynes, Steven J. Miller +2

Let $f(x)\in \mathbb{Z}[x]$; for each integer $\alpha$ it is interesting to consider the number of iterates $n_{\alpha }$, if possible, needed to satisfy $f^{n_{\alpha }}(\alpha )=\alpha$. The sets $\{α, f(α),…