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On the integrability of polynomial 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 equations related with special functions such as Hypergeometric and Heun ones. The Poincaré problem for some families is also approached.

preprint2012arXivOpen access
Primitivo B. Acosta-HumánezJ. Tomás Lázaro-OchoaJuan J. Morales-RuizChara Pantazi
math.DS
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Primitivo B. Acosta-HumánezJ. Tomás Lázaro-OchoaJuan J. Morales-RuizChara Pantazi

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