The dynamics of a function family over quadratic extensions of finite fields

Fabio E. Brochero Martínez, Hugo R. Teixeira

Let ${\mathbb{F}}_q$ be the finite field with $q=p^s$ elements, where $p$ is an odd prime and $s$ a positive integer. In this paper, we define the function $f(X)=(cX^q+aX)(X^{q}-X)^{…