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...
| Autores: | , , |
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| 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 |
| 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. |
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