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On the Singularities of the Planar Cubic Polynomial Differential Systems and the Euler Jacobi Formula

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Abstract

Using the Euler–Jacobi formula we obtain an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar cubic polynomial differential systems when these systems have nine finite singular points.

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Acknowledgements

Agència de Gestió d’Ajuts Universitaris. The first author is supported by the Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación Grant MTM2016-77278-P (FEDER), the Agència de Gestió d’Ajuts Universitaris i de Recerca Grant 2017SGR1617, and the H2020 European Research Council Grant MSCA-RISE-2017-777911. The second author is partially supported by FCT/Portugal through UID/MAT/04459/2019.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Catalonia, Spain

    Jaume Llibre

  2. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1049-00, Lisbon, Portugal

    Claudia Valls

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  1. Jaume Llibre
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  2. Claudia Valls
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Correspondence to Jaume Llibre.

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Llibre, J., Valls, C. On the Singularities of the Planar Cubic Polynomial Differential Systems and the Euler Jacobi Formula. Qual. Theory Dyn. Syst. 19, 96 (2020). https://doi.org/10.1007/s12346-020-00435-9

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  • DOI: https://doi.org/10.1007/s12346-020-00435-9

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