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On the local analytic integrability at the singular point of a class of Liénard analytic differential systems

Authors: Jaume Llibre and Clàudia Valls
Journal: Proc. Amer. Math. Soc. 138 (2010), 253-261
MSC (2000): Primary 34C05, 34A34, 34C14
Published electronically: August 19, 2009
MathSciNet review: 2550190
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Abstract: We consider the Liénard analytic differential systems $ \dot x = y$, $ \dot y= -cx -f(x)y$, with $ c \in \mathbb{R}$ and $ f: \mathbb{R}\to \mathbb{R}$ an analytic function. Then for such systems we characterize the existence of local analytic first integrals in a neighborhood of the singular point located at the origin.

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Additional Information

Jaume Llibre
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella- terra, Barcelona, Catalonia, Spain

Clàudia Valls
Affiliation: Departamento de Matemática, Instituto Superior Técnico, 1049–001 Lisboa, Portugal

Keywords: Analytic integrability, local analytic integrability, Li\'{e}nard differential system
Received by editor(s): February 21, 2009
Received by editor(s) in revised form: April 30, 2009
Published electronically: August 19, 2009
Communicated by: Yingfei Yi
Article copyright: © Copyright 2009 American Mathematical Society