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

• Llibre, Jaume ^[1] ; Valls, Claudia ^[2]
  1. [1] Universitat Autònoma de Barcelona

     Universitat Autònoma de Barcelona

     Barcelona, España

     
  2. [2] Universidade de Lisboa

     Universidade de Lisboa

     Socorro, Portugal

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 3, 2020
• Idioma: inglés
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• Resumen

  • 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.