On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory

Details On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory

2010-12-21

arxiv.org/abs/1012.4796v3

Mathematics

Dynamical Systems

32 pages

Scientific paper

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, Li\'enard equations and equations related with special functions such as Hypergeometric and Heun ones. The Poincar\'e problem for some families is also approached.

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