Estimating the number of limit cycles for one step perturbed homogeneous degenerate centers

• M. MolaeiDerakhtenjani ^[1] ; O. RabieiMotlagh ^[1] ; Haji Mohammad Mohammadinejad ^[1]
  1. [1] University of Birjand

     University of Birjand

     Irán

     
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 38, Nº 1, 2023, págs. 85-104
• Idioma: inglés
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• Resumen

  • We consider a homogeneous degenerate center of order 2m + 1 and perturb it by a homogeneous polynomial of order 2m. We study the Lyapunov constants around the origin to estimate the number of limit cycles. To do it, we classify the parameters and study their effect on the number of limit cycles. Finally, we find that the perturbed degenerate center without any condition has at least two limit cycles, and the number of the bifurcated limit cycles could reach 2m + 3.