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Regular and Chaotic Dynamics, 2017, Volume 22, Issue 5, Pages 543–550
DOI: https://doi.org/10.1134/S1560354717050057 (Mi rcd274) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Darboux Polynomials, Balances and Painlevé Property

Jaume Llibrea, Clàudia Vallsb

a 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
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DOI: https://doi.org/10.1134/S1560354717050057
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.
Funding agency Grant number
Ministerio de Economía y Competitividad de España MTM2016-77278-P
MTM2013-40998-P
Fundação para a Ciência e a Tecnologia UID/MAT/04459/2013
The first author is partially supported by a FEDER-MINECO grant MTM2016-77278-P, a MINECO grant MTM2013-40998-P, and an AGAUR grant number 2014SGR-568. The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013.
Received: 25.05.2017
Accepted: 26.07.2017
Bibliographic databases:
Document Type: Article
MSC: 34A05, 34C05, 37C10
Language: English
Citation: Jaume Llibre, Clàudia Valls, “Darboux Polynomials, Balances and Painlevé Property”, Regul. Chaotic Dyn., 22:5 (2017), 543–550
Citation in format AMSBIB
\Bibitem{LliVal17}
\by Jaume Llibre, Cl\`audia Valls
\paper Darboux Polynomials, Balances and Painlevé Property
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 5
\pages 543--550
\mathnet{http://mi.mathnet.ru/rcd274}
\crossref{https://doi.org/10.1134/S1560354717050057}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85030159687}
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  • https://www.mathnet.ru/eng/rcd274
  • https://www.mathnet.ru/eng/rcd/v22/i5/p543
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:46
     
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