Perturbation of a Period Annulus Bounded by a Saddle–Saddle Cycle in a Hyperelliptic Hamiltonian Systems of Degree Seven

• Yang, Sumin ^[1] ; Qin Bin ^[1] ; Xia Guoen ^[1] ; Yong-Hui, Xia ^[2]
  1. [1] Guangxi University of Finance and Economics

     Guangxi University of Finance and Economics

     China

     
  2. [2] Zhejiang Normal University

     Zhejiang Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
• Idioma: inglés
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• Resumen

  • In this paper, we study the limit cycle bifurcation by perturbing the period annuluses of two perturbed hyper-elliptic Hamiltonian systems of degree seven. The period annuluses are bounded by heteroclinic loops, inside or outside of which there exist two nilpotent cusps. The bifurcation function is Abelian integral which is the first-order approximation of the Poincaré map. The sharp bounds of the number of limit cycles bifurcated from the periodic annuluses are obtained by Chebyshev criterion and asymptotic analysis.