The generalized Liénard polynomial differential systems x'=y,y'= -g(x) - f (x)y with deg g = deg f 1 are not Liouvillian integrable

We prove the nonexistence of Liouvillian first integrals for the generalized Li\'enard polynomial differential systems of the form x' = y, y'=-g(x)-f(x)y, where g(x) and f(x) are arbitrary polynomials such that g = f 1.

Detalhes bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Valls, Clàudia|||0000-0001-8279-1229
Tipo de documento: artigo
Data de publicação:2015
País:España
Recursos:Universitat Autònoma de Barcelona
Repositório:Dipòsit Digital de Documents de la UAB
Idioma:inglês
OAI Identifier:oai:ddd.uab.cat:145352
Acesso em linha:https://ddd.uab.cat/record/145352
https://dx.doi.org/urn:doi:10.1016/j.bulsci.2014.08.010
Access Level:Acceso aberto
Palavra-chave:Darboux polynomial
Exponential factor
Liénard polynomial differential system
Liouvillian first integrals
Descrição
Resumo:We prove the nonexistence of Liouvillian first integrals for the generalized Li\'enard polynomial differential systems of the form x' = y, y'=-g(x)-f(x)y, where g(x) and f(x) are arbitrary polynomials such that g = f 1.