一平面Hamilton系统的Abel积分零点的个数估计

Estimation of Number of Zeros of Abel Integrals of a Planar Hamiltonian System

文中讨论了Hamilton系统的Abel积分的代数构造,证明了I(h)可表为两个生成元I0和I2的线性组合.利用Picard-Fuchs方程和广义罗尔定理,得到了Abel积分的零点个数上界为[3n+1 2].

This paper studies the algebra construction of Abel integrals of Hamiltonian system and proves I（h） is the linear combination of I0andI2.We obtain that the upper bound of the zero number is [3n＋1/2] by Picard-Fuchs equation and generalized Rolle＇s Theorem.