Abstract
We improve the known expressions of the $\mathcal {C}^r$ differential systems in the plane having a given $\mathcal {C}^{r+1}$ invariant curve, or a given $\mathcal {C}^{r+1}$ first integral. Their application to polynomial differential systems having either an invariant algebraic curve, or a first integral, also improves the known results on such systems.
Citation
Antoni Ferragut. Jaume Llibre. "Invariant curves and integrability of planar $\mathcal C^r$ differential systems." Rocky Mountain J. Math. 48 (5) 1537 - 1550, 2018. https://doi.org/10.1216/RMJ-2018-48-5-1537
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