Integrability of complex planar systems with homogeneous nonlinearities

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2016Suggested citation
Fercec, Brigita;
Giné, Jaume;
Romanovski, Valery G.;
Edneral, Victor F.;
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(2016)
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Integrability of complex planar systems with homogeneous nonlinearities.
Journal of Mathematical Analysis and Applications, 2016, vol. 434, núm. 1, p. 894-914.
https://doi.org/10.1016/j.jmaa.2015.09.037.
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In this paper we obtain sufficient conditions for the existence of a local analytic first integral for a family of quintic systems having homogeneous nonlinearities. The family studied in this work is the largest one classified until now for systems with such nonlinearities. We propose also an approach to find reversible systems within polynomial families of Lotka-Volterra systems with homogeneous nonlinearities.