The Integrability and Linearizability of Cubic -Equivariant Systems with Two 1: Resonant Saddle Points

• Xiongkun Wang ^[1] ; Changjian Liu ^[1]
  1. [1] Sun Yat-sen University

     Sun Yat-sen University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01128-3
• Enlaces
  • Texto completo
• Resumen

  • In this article, the integrability and linearizability of a class of cubic Z2-equivariant systems ˙ x = −1 2 x − a21 y + 1 2 x3 + a21x2 y + a12xy2 + a03 y3, ˙y = (−q − b21)y + b21x2 y + b12xy2 + b03 y3, are studied. For any positive integer q, we obtain the first three saddle quantities of the above systems by theoretical analysis. Moreover, for any positive integer q, we derive the necessary and sufficient conditions for the linearizability of the above systems under some assumptions.

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