This article is cited in 2 papers

Darboux Polynomials, Balances and Painlevé Property

Jaume Llibre^a, Clàudia Valls<sup>b

a</sup> Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
^b Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1049–001, Lisboa, Portugal

Abstract: 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.

MSC: 34A05, 34C05, 37C10

Received: 25.05.2017
Accepted: 26.07.2017

Language: English

DOI: 10.1134/S1560354717050057

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