Abstract
We characterize all the planar polynomial differential systems with a unique invariant algebraic curve given by a real conic and having a Darboux invariant.
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The first author is partially supported by the MINECO/FEDER grant MTM2008-03437, the Generalitat de Catalunya Grant 2009SGR-410, ICREA Academia, and two Grants FP7-PEOPLE-2012-IRSES 316338 and 318999. The second author is supported by CNPq-Brazil Grant 308315/2012-0 and by FAPESP Grant 12/18413-7. The third author is supported by FAPESP Grant 2013/01743-7. All the authors are supported by the Int. Coop. Proj. CAPES/MECD-TQED II and PHB-2009-0025.
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Llibre, J., Messias, M. & Reinol, A.C. Darboux invariants for planar polynomial differential systems having an invariant conic. Z. Angew. Math. Phys. 65, 1127–1136 (2014). https://doi.org/10.1007/s00033-013-0390-5
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DOI: https://doi.org/10.1007/s00033-013-0390-5