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Pàgina inicial > Articles > Articles publicats > On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory |
Data: | 2015 |
Resum: | 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. |
Ajuts: | Ministerio de Ciencia e Innovación MTM2009-06973 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-859 Ministerio de Ciencia e Innovación MTM2008-03437 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Differential Galois Theory ; Darboux theory of Integrability ; Poincaré problem ; Rational first integral ; Integrating factor ; Riccati equation ; Liénard Equation ; Liouvillian solution |
Publicat a: | Discrete and continuous dynamical systems. Series A, Vol. 35, Issue 5 (May 2015) , p. 1767-1800, ISSN 1553-5231 |
Postprint 32 p, 490.7 KB |