Generic Complex Polynomial Vector Fields with Real Coefficients

• Jonathan Godin ^[1] ; Christiane Rousseau ^[2]
  1. [1] Université de Moncton

     Université de Moncton

     Canadá

     
  2. [2] University of Montreal

     University of Montreal

     Canadá

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
• Idioma: inglés
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• Resumen

  • The paper studies the complex 1-dimensional polynomial vector fields with real coefficients under topological orbital equivalence preserving the separatrices of the pole at infinity. The number of generic strata is determined, and a complete parametrization of these strata is given in terms of a modulus formed by a combinatorial and an analytic part. The bifurcation diagram is described for the degree 4. A realization theorem is proved for any generic modulus.