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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Liouvillian first integrals for Liénard polynomial differential systems


Authors: J. Llibre and C. Valls
Journal: Proc. Amer. Math. Soc. 138 (2010), 3229-3239
MSC (2010): Primary 37K10, 34D30
Published electronically: April 9, 2010
MathSciNet review: 2653953
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Abstract: We characterize the Liouvillian first integrals for the Liénard polynomial differential systems of the form $ x' = y$, $ y'=-c x-f(x)y$, with $ c \in \mathbb{R}$ and $ f(x)$ is an arbitrary polynomial. For obtaining this result we need to find all the Darboux polynomials and the exponential factors of these systems.


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Additional Information

J. Llibre
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella- terra, Barcelona, Catalonia, Spain
Email: jllibre@mat.uab.cat

C. Valls
Affiliation: Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1049-001, Lisboa, Portugal
Email: cvalls@math.ist.utl.pt

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10338-4
PII: S 0002-9939(10)10338-4
Keywords: Darboux polynomials, exponential factors, Liouvillian first integrals, Li\'enard polynomial differential systems
Received by editor(s): September 10, 2009
Received by editor(s) in revised form: December 16, 2009
Published electronically: April 9, 2010
Communicated by: Yingfei Yi
Article copyright: © Copyright 2010 American Mathematical Society