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

• 论文 • 上一篇    

一类Hamiltonian系统的Abelian积分的零点

杨纪华1, 张二丽2   

  1. 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 修回日期:2018-12-07 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(11701306,11601250)、宁夏高等学校一流学科建设(教育学学科)(NXYLXK2017B11)和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(2017GGJS202,2016GGJS190)

Zeros of Abelian Integral for a Kind of Hamiltonian Systems

Yang Jihua1, Zhang Erli2   

  1. 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 Revised:2018-12-07 Published:2019-11-08
  • Supported by:
    Supported by the NSFC (11701306, 11601250), the Construction of First-class Disciplines of Higher Education of Ningxia (pedagogy) (NXYLXK2017B11) and the Young Top-Notch Talent of Ningxia and Training Plan of University Young Key Teacher of Henan Province (2017GGJS202, 2016GGJS190)

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