一类四次Hamilton函数Abel积分的零点个数估计  

Estimation of the Number of Zeros for Abel Integrals of Quadratic Hamiltonian Functions

作　　者：王彦杰 曹勃[1] 洪晓春[2] WANG Yanjie;CAO Bo;HONG Xiaochun(School of Statistics and Mathematics,Ningbo Polytechnic,Ningbo Zhejiang 315800;School of Statistics and Mathematics,Yunnan University of Finance and Economics,Kunming Yunnan 650221,China)

机构地区：[1]宁波职业技术学院数学教研室,浙江宁波315800 [2]云南财经大学统计与数学学院,云南昆明650221

出　　处：《曲靖师范学院学报》2021年第3期11-16,共6页Journal of Qujing Normal University

基　　金：2020年宁波职业技术学院校级课题“四次Hamilton系统的极限环零点个数研究”(NZ21Q017)。

摘　　要：本文运用Picard-Fuchs方程法和Riccati方程法,研究了一类四次Hamilton函数H(x,y)=x^(2)+y^(2)+ax^(2)y^(2)+bx^(4)+cy^(4)的Abel积分零点个数问题,结论表明Abel积分在区间(c/a^(2)-4bc,0)上,其零点个数不超过3[n-1/4]+12[n-3/4]+22.In this paper,we use the Picard-Fuchs equation method and the Riccati equation method to study a class of four-time Hamiltonian function H(x,y)=x^(2)+y^(2)+ax^(2)y^(2)+bx^(4)+cy^(4), the zero number of Abel c integrals of such functions.The conclusion shows that the Abel integral is in the interval(c/a^(2)-4bc,0),the number of zeros does not exceed 3[n-1/4]+12[n-3/4]+22.

关 键 词：HAMILTON系统 ABEL积分 PICARD-FUCHS方程 RICCATI方程 

分 类 号：O175[理学—数学]