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Título:	Liénard equation and its generalizations
Autor/a:	Giné, Jaume
Notas:	In this paper, we first present a survey of the known results on limit cycles and center conditions for Liénard differential systems. Next we propose a generalization of such systems and we study their center conditions and the number of small-amplitude limit cycles that can bifurcate from the origin. Computing the focal values and using Gröbner bases we find the center conditions for such systems up to a certain degree. We also establish a conjecture about the center conditions for such systems when they have arbitrary degree. The author is partially supported by a MINECO/FEDER grant number MTM2014-53703-P and an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204.
Materia(s):	-Center problem -Analytic integrability -Liénard differential systems
Derechos:	(c) World Scientific Publishing, 2017
Tipo de documento:	Artículo Artículo - Versión aceptada
Editor:	World Scientific Publishing
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