Sufficient Conditions to have Global Centers via Branching Theory

• Jaume Giné ^[1] ; Xiao Yang ^[2]
  1. [1] Universitat de Lleida

     Universitat de Lleida

     Lérida, España

     
  2. [2] School of Mathematics and Statistic
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 4, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • It has always been challenging to identify global centers in a planar differential system, despite the recent proposal of a new algorithm to determine such centers. In this paper, we present a novel method for establishing sufficient conditions to achieve a global center. This method is based on determining all the branches that pass through the point at infinity. We apply the method to a specific example to demonstrate how it circumvents the traditional blow-up procedure.

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