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

Autor
Acosta-Humànez, P.; Lazaro, J. Tomás; Morales, J.; Pantazi, C.
Tipus d'activitat
Article en revista
Revista
Discrete and continuous dynamical systems. Series A
Data de publicació
2015-05-01
Volum
35
Número
5
Pàgina inicial
1767
Pàgina final
1800
DOI
https://doi.org/10.3934/dcds.2015.35.1767 Obrir en finestra nova
Projecte finançador
DINAMICA ASOCIADA A CONEXIONES ENTRE OBJETOS INVARIANTES. APLICACIONES A
URL
http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10632 Obrir en finestra nova
Resum
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.
Paraules clau
1st integrals, Darboux theory of integrability, Differential Galois theory, Lienard equation, Liouvillian solution, Poincare problem, Riccati equation, darboux integrating factors, foliations, galois theory, integrating factor, invariant algebraic-curves, inverse problems, linear-differential equations, multiplicity, poincare problem, rational first integral, systems
Grup de recerca
SD - Sistemes Dinàmics de la UPC

Participants