Determining Liouvillian First Integrals for Dynamical Systems in the Plane

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.

References in corpus (3)

• Computer Algebra Solving of First Order ODEs Using Symmetry Methods
• Computer Algebra Solving of Second Order ODEs Using Symmetry Methods
• A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution

Cited by in corpus (4)

• Dealing with Rational Second Order Ordinary Differential Equations where both Darboux and Lie Find It Difficult: The $S$-function Method
• An Efficient Method for Computing Liouvillian First Integrals of Planar Polynomial Vector Fields
• A generalization of the S-function method applied to a Duffing-Van der Pol forced oscillator
• A Semi-Algorithmic Search for Lie Symmetries