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

Jihua Yang, Liqin Zhao

• 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.