一平面Hamilton系统的Abel积分的零点个数估计

Estimation of the Number of Zeros of Abelian Integrals of a Planar Hamiltonian System

中文关键词:  Hamilton系统  Abel积分  Picard-Fuchs方程

英文关键词:Hamiltonian system  Abelian integrals  Picard-Fuchs equation.

中文摘要:

      本文讨论一平面Hamilton系统在一般n次多项式扰动下的系统的Abel积分的零点个数估计问题,得到的结论是:该系统的Abel积分的零点个数的上界为[(3n-1)/2]。

英文摘要:

      In this paper, we study the number of zeros of Abelian integrals of a planar Hamil-tonian system when we perturb it inside the class of all polynomial systems of degree n. We obtain that the upper bound of the number is [(3n-1)/2].