In this paper we describe the structure of the graphs associated with the map $\theta: x \mapsto x + x^{-1}$ over finite fields of characteristic three and five. While in characteristic three the map $\theta$ is conjugated to the inverse of the square mapping, in characteristic five it is related to an endomorphism of a certain elliptic curve.
Graphs associated with the map in finite fields of characteristic three and five
UGOLINI, Simone
2013-01-01
Abstract
In this paper we describe the structure of the graphs associated with the map $\theta: x \mapsto x + x^{-1}$ over finite fields of characteristic three and five. While in characteristic three the map $\theta$ is conjugated to the inverse of the square mapping, in characteristic five it is related to an endomorphism of a certain elliptic curve.
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