On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some families of quadratic vector fields, Liénard equations and equatio...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:221035 |
| Acceso en línea: | https://ddd.uab.cat/record/221035 https://dx.doi.org/urn:doi:10.3934/dcds.2015.35.1767 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential Galois Theory Darboux theory of Integrability Poincaré problem Rational first integral Integrating factor Riccati equation Liénard Equation Liouvillian solution |
| Sumario: | We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some families of quadratic vector fields, Liénard equations and equations related with special functions such as Hypergeometric and Heun ones. The Poincaré problem for some families is also approached. |
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