一类具有幂零中心四次Hamiltonian的Abelian积分的零点个数

数学物理学报 ›› 2016, Vol. 36 ›› Issue (5): 937-945.

一类具有幂零中心四次Hamiltonian的Abelian积分的零点个数

杨纪华, 刘媚, 何志成

宁夏师范学院数学与计算机科学学院宁夏固原 756000

收稿日期:2015-12-05 修回日期:2016-06-07 出版日期:2016-10-26 发布日期:2016-10-26
作者简介:杨纪华,E-mail:jihua1113@163.com
基金资助:
国家自然科学基金（11361046，11271046）和宁夏科技支撑计划项目（KJ[2015]26（4））资助

The Number of Zeros of Abelian Integrals for a Kind of Quartic Hamiltonians with a Nilpotent Center

Yang Jihua, Liu Mei, He Zhicheng

Department of Mathematics and Computer Science, Ningxia Normal University, Ningxia Guyuan 756000

Received:2015-12-05 Revised:2016-06-07 Online:2016-10-26 Published:2016-10-26
Supported by:
Supported by the NSFC (11361046, 11271046) and the Science and Technology Pillar Program of Ningxia(KJ[2015]26(4))

摘要/Abstract

摘要：

该文证明了Hamiltonian H(x，y)=-x²+ax²y²+bx⁴+cy⁴的Abelian积分在区间((c)/(a²-4bc)，0)上零点的个数不超过3n+3[(n-1)/(4)]+14(计重数)，其中a>0，b<-2，c<0，a²>4bc.

关键词: Hamiltonian, Abelian积分, Picard-Fuchs方程, 幂零中心

Abstract:

In this paper, we prove that the number of zeros of Abelian integral for the Hamiltonians H(x,y)=-x²+ax²y²+bx⁴+cy⁴ on the interval (0,(c)/(a²-4bc)) is not more than 3n+3[(n-1)/(4)]+14 (taking into account the multiplicity), where a>0,b<-2,c<0,a²>4bc.

Key words: Hamiltonian, Abelian integral, Picard-Fuchs equation, Nilpotent center

中图分类号:

O175

杨纪华, 刘媚, 何志成. 一类具有幂零中心四次Hamiltonian的Abelian积分的零点个数[J]. 数学物理学报, 2016, 36(5): 937-945.

Yang Jihua, Liu Mei, He Zhicheng. The Number of Zeros of Abelian Integrals for a Kind of Quartic Hamiltonians with a Nilpotent Center[J]. Acta mathematica scientia,Series A, 2016, 36(5): 937-945.

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