Integrability of Liénard systems with a weak saddle
Issue date
2017Suggested citation
Gasull i Embid, Armengol;
Giné, Jaume;
.
(2017)
.
Integrability of Liénard systems with a weak saddle.
Zeitschrift für angewandte Mathematik und Physik, 2017, vol. 68, núm. 13, p 1-13.
https://doi.org/10.1007/s00033-016-0756-6.
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We characterize the local analytic integrability of weak saddles for complex Lienard systems, x˙ = y−F(x), y˙ = ax,
0 = a ∈ C, with F analytic at 0 and F(0) = F (0) = 0. We prove that they are locally integrable at the origin if and only if
F(x) is an even function. This result implies the well-known characterization of the centers for real Lienard systems. Our
proof is based on finding the obstructions for the existence of a formal integral at the complex saddle, by computing the
so-called resonant saddle quantities
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Zeitschrift für angewandte Mathematik und Physik, 2017, vol. 68, núm. 13, p 1-13European research projects
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