Finite Cyclicity of Some Graphics Through a Nilpotent Point of Saddle Type Inside Quadratic Systems

Christiane Rousseau ^[1] ; Chunhua Shan ^[2] ; Huaiping Zhu ^[3]
1. [1] University of Montreal
  
  University of Montreal
  
  Canadá
2. [2] University of Alberta
  
  University of Alberta
  
  Canadá
3. [3] York University (Canadá)
  
  York University (Canadá)
  
  Canadá
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Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 15, Nº 1, 2016, págs. 237-256
Idioma: inglés
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Resumen
- In this paper we show the finite cyclicity of the two graphics (I 1 12) and (I 1 13) through a triple nilpotent point of saddle type inside quadratic vector fields.
  
  These results contribute to the program launched in 1994 by Dumortier, Roussarie and Rousseau (DRR program) to show the existence of a uniform upper bound for the number of limit cycles for planar quadratic vector fields.