Polynomial and rational first integrals for planar quasi-homogeneous polynomial differential sytems

In this paper we find necessary and sufficient conditions in order that a planar quasi-homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi-homogeneous polynomial differential system can be transformed into a differential syste...

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Detalhes bibliográficos
Autores: Giné, Jaume|||0000-0001-7109-2553, Grau, Maite|||0000-0002-1937-9220, Llibre, Jaume|||0000-0002-9511-5999
Tipo de documento: artigo
Data de publicação:2013
País:España
Recursos:Universitat Autònoma de Barcelona
Repositório:Dipòsit Digital de Documents de la UAB
Idioma:inglês
OAI Identifier:oai:ddd.uab.cat:150596
Acesso em linha:https://ddd.uab.cat/record/150596
https://dx.doi.org/urn:doi:10.3934/dcds.2013.33.4531
Access Level:Acceso aberto
Palavra-chave:Quasi-homogeneous polynomial differential equations
Integrability problem
Polynomial first integral
Rational first integral
Descrição
Resumo:In this paper we find necessary and sufficient conditions in order that a planar quasi-homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi-homogeneous polynomial differential system can be transformed into a differential system of the form u˙ = uf(v), ˙v = g(v) with f(v) and g(v) polynomials, and vice versa.