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, Lienard equations and equatio...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/129783 |
| Acceso en línea: | https://hdl.handle.net/2117/129783 https://dx.doi.org/10.3934/dcds.2015.35.1767 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebra Differential Galois theory Darboux theory of integrability Poincare problem rational first integral integrating factor Riccati equation Lienard equation Liouvillian solution invariant algebraic-curves linear-differential equations darboux integrating factors inverse problems 1st integrals poincare problem galois theory systems foliations multiplicity Àlgebra diferencial Àrees temàtiques de la UPC::Matemàtiques i estadística |
| 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, Lienard equations and equations related with special functions such as Hypergeometric and Heun ones. The Poincare problem for some families is also approached. |
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