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Jaume Llibre, Xiang Zhang (2002)
Polynomial first integrals for quasi-homogeneous polynomial differential systemsNonlinearity, 15
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N. Kudryashov (2015)
Analytical solutions of the Lorenz systemRegular and Chaotic Dynamics, 20
For a given polynomial differential system we provide different necessary conditions for the existence of Darboux polynomials using the balances of the system and the Painlevé property. As far as we know, these are the first results which relate the Darboux theory of integrability, first, to the Painlevé property and, second, to the Kovalevskaya exponents. The relation of these last two notions to the general integrability has been intensively studied over these last years.
Regular and Chaotic Dynamics – Springer Journals
Published: Oct 1, 2017
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