On projective systems of rational difference equations

TL;DR

This paper studies a special class of rational difference equations called projective systems, which map lines through the origin into lines through the origin, and introduces a change of variables to analyze their behavior.

Contribution

It introduces a new change of variables for analyzing projective systems of rational difference equations, facilitating understanding of their dynamics.

Findings

Change of variables simplifies analysis of projective systems.

Examples demonstrate the effectiveness of the method.

Provides insights into the behavior of these systems.

Abstract

We discuss first order systems of rational difference equations which have the property that lines through the origin are mapped into lines through the origin. We call such systems projective systems of rational difference equations and we show a useful change of variables which helps us to understand the behavior in these cases. We include several examples to demonstrate the utility of this change of variables.