On the functional graph of $f(X)=c(X^{q+1}+aX^2)$ over quadratic extensions of finite fields (2111.11132v1)

Abstract: Let $\mathbb{F}q$ be the finite field with $q$ elements and $char(\mathbb{F}_q)$ odd. In this article we will describe completely the dynamics of the map $f(X)=c(X^{q+1}+aX^2)$, for $a={\pm1}$ and $c\in\mathbb{F}_q^*$, over the finite field $\mathbb{F}{q^2}$, and give some partial results for $a\in\mathbb{F}_q^*\setminus{\pm1}$.