Polynomial and rational first integrals for planar homogeneous polynomial differential systems

In this paper we find necessary and sufficient 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|||0000-0001-7109-2553, Grau, Maite|||0000-0002-1937-9220, Llibre, Jaume|||0000-0002-9511-5999
Format: article
Publication Date:2014
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:150716
Online Access:https://ddd.uab.cat/record/150716
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_Extra14_14
Access Level:Open access
Keyword:First integral
Integrability problem
Polynomial differential equations
Description
Summary:In this paper we find necessary and sufficient 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.