On the planar integrable differential systems
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Issue date
2011Suggested citation
Giné, Jaume; Llibre, Jaume; . (2011) . On the planar integrable differential systems. ZAMP. Journal of Applied Mathematics and Physics, 2011, vol. 62, núm. 4, p. 567-574. https://doi.org/10.1007/s00033-011-0116-5.
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Abstract
Under very general assumptions we prove that the planar differential systems having a first integral are essentially the linear differential systems u˙ = u, ˙v = v. Additionally such systems always have a Lie symmetry. We improve these results for polynomial differential systems defined in R2 or C2.