Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system

• Autores: Jibin Li, Zhenrong Liu
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 35, Nº 2, 1991, págs. 487-506
• Idioma: inglés
• Títulos paralelos:
  • Conjunto de bifurcación y ciclos límite que forman ojos compuestos en un sistema hamiltoniano perturbado
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• Resumen

  • In this paper we consider a class of perturbation of a Hamiltonian cubic system with 9 finite critical points. Using detection functions, we present explicit formulas for the global and local bifurcations of the flow. We exhibit various patterns of compound eyes of limit cycles. These results are concerned with the weakened Hilbert's 16th problem posed by V. I. Arnold in 1977.