On the local analytic integrability at the singular point of a class of Liénard analytic differential systems
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- by Jaume Llibre and Clàudia Valls PDF
- Proc. Amer. Math. Soc. 138 (2010), 253-261 Request permission
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.References
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Additional Information
- Jaume Llibre
- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella-terra, Barcelona, Catalonia, Spain
- MR Author ID: 115015
- ORCID: 0000-0002-9511-5999
- Email: jllibre@mat.uab.cat
- Clàudia Valls
- Affiliation: Departamento de Matemática, Instituto Superior Técnico, 1049–001 Lisboa, Portugal
- MR Author ID: 636500
- Email: cvalls@math.ist.utl.pt
- 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
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 253-261
- MSC (2000): Primary 34C05, 34A34, 34C14
- DOI: https://doi.org/10.1090/S0002-9939-09-10036-9
- MathSciNet review: 2550190