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Configurations of the Topological Indices of the Planar Polynomial Differential Systems of Degree (2, m)

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Abstract

Using the Euler–Jacobi formula there is a 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 polynomial differential systems \(\dot{x}=P(x,y)\), \(\dot{y} =Q(x,y)\) with degree of P equal to 2 and degree of Q equal to m when these systems have 2m finite singular points.

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Acknowledgements

The first author is supported by the Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación grants MTM2016-77278-P (FEDER) and PID2019-104658GB-I00 (FEDER), the Agència de Gestó 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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  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193, Barcelona, Catalonia, Spain

    Jaume Llibre

  2. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    Claudia Valls

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

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Llibre, J., Valls, C. Configurations of the Topological Indices of the Planar Polynomial Differential Systems of Degree (2, m). Results Math 76, 21 (2021). https://doi.org/10.1007/s00025-020-01322-0

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  • DOI: https://doi.org/10.1007/s00025-020-01322-0

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