一类三次Hamilton系统的Abel积分的渐近性态  

Asymptotic Property of the Abel Integral in one Cubic Hamilton System

作　　者：郭丽伟 

机构地区：[1]锦州师范高等专科学校教务处,辽宁锦州121000

出　　处：《沈阳工程学院学报（自然科学版）》2013年第3期275-278,共4页Journal of Shenyang Institute of Engineering:Natural Science

摘　　要：当今分岔理论研究的热门课题之一,是确定Abel积分I(h)的零点个数上界问题.这一问题和确定Hamilton向量场在多项式扰动下的极限环个数有着密切关系.而求得I(h)在定义域端点的渐近展式,对研究I(h)的性质起着重要作用.这里利用常微分方程解析理论,讨论一类三次Hamilton系统在三次多项式扰动下的Abel积分的渐近性态,求得I(h)在定义域端点的渐近展式.Nowadays,to determine the upper bound of the number of zero of the Abel integral I（h） is one of the most popular subjects in bifurcation theory research.The subject has a close relation with determining the number of limit cycles of Hamilton vector field with polynomial perturbation.To find the progressive extensible formula of I（h）at the endpoint of domain has a significant role in research the nature of I（h）.Using ordinary differential equations theory,the article discussed the asymptotic behavior of Abel integral with the cubic polynomial perturbation of a class of cubic Hamilton system and found the progressive extensible formula of I（h） at the endpoint of domain.

关 键 词：HAMILTON系统 ABEL积分 PICARD-FUCHS方程 渐近展式 

分 类 号：O175[理学—数学]