Abstract
We consider a complex differential system with a weak saddle at the origin and we characterize the existence of a local analytic first integral around the weak saddle. If the system does not have a fixed degree and instead the degree is arbitrarily large, the family can have a numerable infinite number of integrability cases.
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Acknowledgments
The authors are grateful to the referee for his/her valuable comments and suggestions to improve this paper.
Funding
The first author is partially supported by a MINECO/ FEDER grant number MTM2017-84383-P and an AGAUR (Generalitat de Catalunya) grant number 2017SGR-1276. The second author is supported by FCT/Portugal through UID/MAT/04459/2013.
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Giné, J., Valls, C. Integrability Conditions of a Weak Saddle in a Complex Polynomial Differential System. J Dyn Control Syst 28, 91–108 (2022). https://doi.org/10.1007/s10883-020-09525-y
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DOI: https://doi.org/10.1007/s10883-020-09525-y