Functional graphs of rational maps induced by endomorphisms of ordinary elliptic curves over finite fields

TL;DR

This paper investigates the behavior of rational functions generated by endomorphisms of ordinary elliptic curves over finite fields, exploring their dynamic properties and structural characteristics.

Contribution

It introduces a detailed analysis of the functional graphs formed by these rational maps, highlighting new insights into their structure and dynamics.

Findings

Characterization of the graph structures induced by elliptic curve endomorphisms

Identification of specific dynamic behaviors of these rational maps

Insights into the algebraic and combinatorial properties of the graphs

Abstract

In this paper we study the dynamics of rational maps induced by endomorphisms of ordinary elliptic curves defined over finite fields.