Elsevier

Applied Mathematics Letters

Volume 70, August 2017, Pages 39-45
Applied Mathematics Letters

On the integrability of Liénard systems with a strong saddle

https://doi.org/10.1016/j.aml.2017.03.004Get rights and content
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Abstract

We study the local analytic integrability for real Liénard systems, ẋ=yF(x), ẏ=x, with F(0)=0 but F(0)0, which implies that it has a strong saddle at the origin. First we prove that this problem is equivalent to study the local analytic integrability of the [p:q] resonant saddles. This result implies that the local analytic integrability of a strong saddle is a hard problem and only partial results can be obtained. Nevertheless this equivalence gives a new method to compute the so-called resonant saddle quantities transforming the [p:q] resonant saddle into a strong saddle.

Keywords

Center problem
Analytic integrability
Strong saddle
Liénard equation
Resonant saddle

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