Graphs associated with the map $x \mapsto x+x^{-1}$ in finite fields of characteristic five

TL;DR

This paper investigates the structure of graphs generated by iterating the map x ↦ x + x^{-1} over finite fields of characteristic five, revealing new insights into their properties and behavior.

Contribution

It provides a detailed analysis of the graph structures associated with the map in characteristic five, a topic not extensively explored before.

Findings

Characterization of the graph components

Identification of cycle structures

Insights into the dynamics of the map

Abstract

In this paper we study the structure of the graphs associated with the iterations of the map $x \mapsto x+x^{-1}$ over finite fields of characteristic five.