On the functional graph of f(X)=c(Xq+1 + aX2) over quadratic extensions of finite fields

F.E Brochero Martínez,H.R Teixeira

doi:10.1016/j.ffa.2023.102180

On the functional graph of f(X)=c(Xq+1 + aX2) over quadratic extensions of finite fields

F.E Brochero Martínez, H.R Teixeira

https://doi.org/10.1016/j.ffa.2023.102180

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Journal: Finite Fields and Their Applications

Publication Date: Mar 13, 2023

Affiliation: Carleton University

#Finite Field #Extensions Of Fields + Show 4 more

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Abstract

Let Fq be the finite field with q elements and char(Fq) odd. In this article we will describe completely the dynamics of the map f(X)=c(Xq+1+aX2) over the finite field Fq2, for a∈{±1} and c∈Fq⁎. We will also give some partial results for a∈Fq⁎∖{±1}.

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