© 2017 Elsevier Ltd We study the local analytic integrability for real Liénard systems, ẋ=y−F(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.
|Journal||Applied Mathematics Letters|
|Publication status||Published - 1 Aug 2017|
- Analytic integrability
- Center problem
- Liénard equation
- Resonant saddle
- Strong saddle