The Number of Periodic Orbits of a Rational Difference Equation

TL;DR

This paper introduces a method using a variant of the Lefschetz Fixed Point Theorem to count periodic orbits in specific rational difference equations, providing a new analytical tool for dynamical systems analysis.

Contribution

It applies a modified Lefschetz Fixed Point Theorem to effectively count periodic orbits in rational difference equations, offering a novel approach in the field.

Findings

Successfully counts periodic orbits in selected rational difference equations

Demonstrates the applicability of topological fixed point theorems in discrete dynamical systems

Provides a new analytical framework for studying periodic behavior

Abstract

We show how a variant of the Lefschetz Fixed Point Theorem may be used to count the number of periodic orbits for certain rational difference equations.