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<p>This paper presents an analysis of lower bounds on local criticality within the family of piecewise quadratic reversible centers. Through a study of perturbations within this class, we determine that a minimum of five (in the linear case) or four (in the nonlinear case) local critical periods can bifurcate from the isochronous center. Notably, five represents the highest level of weakness observed in this context.</p>

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Period function of planar piecewise reversible quadratic systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月10日

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  • Alex C. Rezende,
  • Mirianne A. S. Santos,
  • Joan Torregrosa

摘要

This paper presents an analysis of lower bounds on local criticality within the family of piecewise quadratic reversible centers. Through a study of perturbations within this class, we determine that a minimum of five (in the linear case) or four (in the nonlinear case) local critical periods can bifurcate from the isochronous center. Notably, five represents the highest level of weakness observed in this context.