一类三次哈密尔顿系统阿贝尔积分零点个数的估计  

ESTIMATION OF THE NUMBER OF ZEROS OF ABELIAN INTEGRAL FOR A KIND OF CUBIC HAMILTON SYSTEM

作　　者：王娜[1] 赵丽琴[2] 

机构地区：[1]上海交通大学理学院数学系,上海200240 [2]北京师范大学数学科学学院,北京100875

出　　处：《北京师范大学学报（自然科学版）》2014年第3期234-238,共5页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11271046)

摘　　要：研究一类三次椭圆Hamilton系统在完全三次多项式下的扰动,证明了如下结论:1)围绕全局中心定义的Abel积分的孤立零点个数不超过7;2)围绕双同宿轨定义的Abel积分的孤立零点个数不超过6.Perturbations from a kind of cubic Hamilton system under general cubic polynomials were investigated.It is proved that：1）The number of isolated zeros of related Abelian integrals around the center is not more than 7 for global center;2 ）The number of isolated zeros of related Abelian integrals outside the double homoclinic loop is not more than 6 for figure eight-loop.

关 键 词：阿贝尔积分 全局中心 双同宿环 

分 类 号：O176.3[理学—数学]