08193 Bellaterra, Barcelona, Catalonia, Spain
Departament de Matemàtiques, Universitat Autònoma de Barcelona
Llibre J., Valls C.
Darboux Polynomials, Balances and Painlevé Property
2017, vol. 22, no. 5, pp. 543-550
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.