Polynomial and rational first integrals for planar homogeneous polynomial differential systems

In this paper we find necessary and suficient conditions in order that a planar homogeneous polynomial differential system has a polynomial or rational first integral. We apply these conditions to linear and quadratic homogeneous polynomial differential systems.

Bibliographic Details
Authors: Giné, Jaume, Grau Montaña, Maite, Llibre, Jaume
Format: article
Status:Versión aceptada para publicación
Publication Date:2014
Country:España
Institution:Universitat de Lleida (UdL)
Repository:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/49445
Online Access:https://doi.org/10.5565/PUBLMAT_Extra14_14
http://hdl.handle.net/10459.1/49445
Access Level:Open access
Keyword:First integral
Polynomial differential equations
Integrability problem
Equacions diferencials
Description
Summary:In this paper we find necessary and suficient conditions in order that a planar homogeneous polynomial differential system has a polynomial or rational first integral. We apply these conditions to linear and quadratic homogeneous polynomial differential systems.