The Perturbation of a Class of Hyper-Elliptic Hamilton System with a Double Eight Figure Loop

• Jihua Yang ^[1] ; Liqin Zhao ^[2]
  1. [1] Ningxia Normal University

     Ningxia Normal University

     China

     
  2. [2] Beijing Normal University

     Beijing Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 2, 2017, págs. 317-360
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper, we consider the upper bounds of the number of isolated zeros of Abelian integrals associated to system x˙ = y, y˙ = − x5 − 5 2 x3 + x under the perturbation of (α0 +α1x +α2x2 +α3x3 +α4x4)y ∂ ∂y , where 0 < || 1 and αi ∈ R,i = 0, 1, 2, 3, 4. The unperturbed system has a double eight figure loop.

    The sharp upper bounds are obtained for ten cases that two of five parameters vanish.