Determining Liouvillian First Integrals for Dynamical Systems in the Plane

TL;DR

This paper introduces an algorithm and software routines in Maple 10 for finding Liouvillian first integrals of planar dynamical systems by reducing them to rational first order ODEs, aiding algebraic analysis.

Contribution

It presents a novel algorithm and Maple implementation for computing Liouvillian first integrals in planar systems, based on reduction to rational first order ODEs.

Findings

Successfully implemented Maple routines for solving rational first order ODEs.

Provides tools for algebraic property analysis of dynamical systems.

Facilitates research in integrability of planar dynamical systems.

Abstract

Here we present/implement an algorithm to find Liouvillian first integrals of dynamical systems in the plane. In \cite{JCAM}, we have introduced the basis for the present implementation. The particular form of such systems allows reducing it to a single rational first order ordinary differential equation (rational first order ODE). We present a set of software routines in Maple 10 for solving rational first order ODEs. The package present commands permitting research incursions of some algebraic properties of the system that is being studied.