On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory
PublisherAmerican Institute of Mathematical Sciences
Rights accessOpen Access
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.
CitationAcosta-Humànez, P. [et al.]. On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory. "Discrete and continuous dynamical systems. Series A", 1 Maig 2015, vol. 35, núm. 5, p. 1767-1800.