On the Number of Hyperelliptic Limit Cycles of Liénard Systems

• Qian Xinjie ^[1] ; Yang Jiazhong ^[1]
  1. [1] Peking University

     Peking University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
• Idioma: inglés
• DOI: 10.1007/s12346-020-00382-5
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we present a systematic study of the maximum number, denoted by H(m, n), of hyperelliptic limit cycles of the Liénard systems x˙=y,y˙=-fm(x)y-gn(x),where, respectively, fm(x) and gn(x) are real polynomials of degree m and n. The main results of the paper are as follows: We give the upper as well as the lower bounds of H(m, n) in all the cases. It turns out that in most cases these bounds are sharp. Furthermore, the configuration of hyperelliptic limit cycles is also explicitly described.

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