Square patterns in dynamical orbits

Vefa Goksel, Giacomo Micheli

Let $q$ be an odd prime power. Let $f\in {\mathbb{F}}_q[x]$ be a polynomial having degree at least $2$, $a\in {\mathbb{F}}_q$, and denote by $f^n$ the $n$-th iteration of $f$. Let $\chi$…