十一次Hamilton系统的Abelian积分零点个数的线性估计  

Linear Estimate for the Number of Zeros of Abelian Integrals of Hamiltonian System with Eleven Degree

作　　者：白龙[1] BAI Long(School of Mathematics and Computer Science,Ningxia Normal University,Guyuan 756000,China)

机构地区：[1]宁夏师范学院数学与计算机科学学院,宁夏固原756000

出　　处：《应用数学》2021年第4期922-928,共7页Mathematica Applicata

基　　金：国家自然基金(11361046)。

摘　　要：本文研究一类十一次Hamilton系统在n次多项式扰动下的Abelian积分的零点个数问题.利用Picard-Fuchs方程法,得到这类扰动Hamilton系统的Abelian积分的零点个数的上界(计重数).In this paper, we study the number of zeros of Abelian integrals for a class of eleven degree Hamiltonian systems with n-degree polynomial perturbations. By using Picard-Fuchs equation method, we derive the upper bound of the number of zeros of Abelian integrals for this class of perturbed Hamiltonian systems(taking into account the multiplicity).

关 键 词：HAMILTON系统 Abelian积分 PICARD-FUCHS方程 

分 类 号：O175[理学—数学]