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

Primitivo B. Acosta-Humánez | Zendy; J. Tomás Lázaro | Zendy; Juan J. Morales-Ruiz | Zendy; Chara Pantazi | Zendy

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

Author(s) -

Primitivo B. Acosta-Humánez,

J. Tomás Lázaro,

Juan J. Morales-Ruiz,

Chara Pantazi

Publication year - 2014

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2015.35.1767

Subject(s) - mathematics , differential galois theory , polynomial , pure mathematics , foliation (geology) , vector field , mathematical analysis , hypergeometric function , differential equation , quadratic equation , plane (geometry) , galois group , embedding problem , geometry , geochemistry , metamorphic rock , geology

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.

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