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<p>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.</p>

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Sufficient Conditions to have Global Centers via Branching Theory

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年6月23日

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  • Jaume Giné,
  • Xiao Yang

摘要

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.