Liouvillian integrability versus Darboux polynomials

In this note we provide a sufficient condition on the existence of Darboux polynomials of polynomial differential systems via existence of Jacobian multiplier or of Liouvillian first integral and a degree condition among different components of the system. As an application of our main results we pr...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Valls, Clàudia|||0000-0001-8279-1229, Zhang, Xiang
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:169448
Acceso en línea:https://ddd.uab.cat/record/169448
https://dx.doi.org/urn:doi:10.1007/s12346-016-0212-1
Access Level:acceso abierto
Palabra clave:Darboux Jacobian multiplier
Darboux polynomial
Liouvillian integrability
Polynomial differential systems
Descripción
Sumario:In this note we provide a sufficient condition on the existence of Darboux polynomials of polynomial differential systems via existence of Jacobian multiplier or of Liouvillian first integral and a degree condition among different components of the system. As an application of our main results we prove that the Liénard polynomial differential system x ̇ = y, y ̇ = - f (x)y - g(x) with deg f.