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32 p, 490.7 KB On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory / Acosta-Humánez, Primitivo B. (Universidad del Atlántico and Intelectual.Co. Department of Mathematics (Colombia)) ; Lázaro, J. Tomás (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I) ; Morales Ruiz, Juan J. (Universidad Politécnica de Madrid. Departamento de Matemática Aplicada) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)
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. [...]
2015 - 10.3934/dcds.2015.35.1767
Discrete and continuous dynamical systems. Series A, Vol. 35, Issue 5 (May 2015) , p. 1767-1800  
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