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arXiv · 2111.11132

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

F. E. Brochero Martínez·H. R. Teixeira
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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 $a\in\mathbb{F}_q^*\setminus\{\pm1\}$.

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F. E. Brochero Martínez, H. R. Teixeira. 2021-11-22. On the functional graph of $f(X)=c(X^{q+1}+aX^2)$ over quadratic extensions of finite fields. https://arxiv.org/abs/2111.11132

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