Darboux Polynomials, Balances and Painlevé Property

    2017, Volume 22, Number 5, pp.  543-550

    Author(s): Llibre J., Valls  C.

    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.
    Keywords: Painlevé property, Darboux polynomial, Kovalevskaya exponents
    Citation: Llibre J., Valls  C., Darboux Polynomials, Balances and Painlevé Property, Regular and Chaotic Dynamics, 2017, Volume 22, Number 5, pp. 543-550

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