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

Llibre, Jaume; Valls, Clàudia

doi:10.1090/S0002-9939-09-10036-9

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.

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