一类Hamiltonian系统的Abelian积分的零点

数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1025-1032.

一类Hamiltonian系统的Abelian积分的零点

杨纪华^1,*(),张二丽²

¹ 宁夏师范学院数学与计算机科学学院宁夏固原 756000
² 郑州财经学院信息工程学院郑州 450001

收稿日期:2018-08-05 出版日期:2019-10-26 发布日期:2019-11-08
通讯作者: 杨纪华 E-mail:jihua1113@163.com
基金资助:
国家自然科学基金(11701306);国家自然科学基金(11601250);宁夏高等学校一流学科建设（教育学学科）(NXYLXK2017B11);宁夏青年拔尖人才和河南省高等学校青年骨干教师培养计划(2017GGJS202);宁夏青年拔尖人才和河南省高等学校青年骨干教师培养计划(2016GGJS190)

Zeros of Abelian Integral for a Kind of Hamiltonian Systems

Jihua Yang^1,*(),Erli Zhang²

¹ School of Mathematics and Computer Science, Ningxia Normal University, Ningxia Guyuan 756000
² School of Information Engineering, Zhengzhou Institute of Finance and Economics, Zhengzhou 450001

Received:2018-08-05 Online:2019-10-26 Published:2019-11-08
Contact: Jihua Yang E-mail:jihua1113@163.com
Supported by:
the NSFC(11701306);the NSFC(11601250);the Construction of First-class Disciplines of Higher Education of Ningxia (pedagogy)(NXYLXK2017B11);the Young Top-Notch Talent of Ningxia and Training Plan of University Young Key Teacher of Henan Province(2017GGJS202);the Young Top-Notch Talent of Ningxia and Training Plan of University Young Key Teacher of Henan Province(2016GGJS190)

摘要/Abstract

摘要：

该文得到了一类Hamiltonian系统的Abelian积分的零点的个数的上界.该Abelian积分有k+2个生成元，并且这些生成元满足两个不同的Picard-Fuchs方程.最后，用两个例子说明理论结果的应用.

关键词: Hamiltonian系统, Abelian积分, Picard-Fuchs方程, Chebyshev空间, Hilbert-Arnold问题

Abstract:

In this paper, we obtain an upper bound of the number of zeros of Abelian integral for a kind of Hamiltonian systems. The Abelian integral has k + 2 generators which satisfy two different Picard-Fuchs equations. Finally, we present two examples to illustrate an application of the theoretical result.

Key words: Hamiltonian system, Abelian integral, Picard-Fuchs equation, Chebyshev space, Hilbert-Arnold problem

中图分类号:

O175

杨纪华,张二丽. 一类Hamiltonian系统的Abelian积分的零点[J]. 数学物理学报, 2019, 39(5): 1025-1032.

Jihua Yang,Erli Zhang. Zeros of Abelian Integral for a Kind of Hamiltonian Systems[J]. Acta mathematica scientia,Series A, 2019, 39(5): 1025-1032.

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