Liouvillian first integrals for Liénard polynomial differential systems

Llibre, J.; Valls, C.

doi:10.1090/S0002-9939-10-10338-4

Liouvillian first integrals for Liénard polynomial differential systems
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by J. Llibre and C. Valls

Proc. Amer. Math. Soc. 138 (2010), 3229-3239

DOI: https://doi.org/10.1090/S0002-9939-10-10338-4

Published electronically: April 9, 2010

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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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