一类单中心三次Hamilton系统的Abel积分零点个数  

Number of zeros of Abelian integral for a class of cubic Hamiltonian systems with single center

作　　者：张永康[1] 李宝毅[1] 隋世友 ZHANG Yongkang;LI Baoyi;SUI Shiyou(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China;School of Science,Tianjin University of Commerce,Tianjin 300134,China)

机构地区：[1]天津师范大学数学科学学院,天津300387 [2]天津商业大学理学院,天津300134

出　　处：《天津师范大学学报（自然科学版）》2023年第6期1-5,共5页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11671040,12101450);天津市自然科学基金资助项目(18JCYBJC85800).

摘　　要：研究一类单中心三次Hamilton系统在n次多项式扰动下的Abel积分零点个数.利用Abel积分代数结构的特殊性,通过连续求导对其进行降阶,得到了Abel积分孤立零点个数较小的上界,改进了相关文献的结果.The number of zeros of Abelian integral for a class of cubic Hamiltonian systems with single center under polynomial perturbation of degree n is studied.By taking advantage of the special algebraic structure of Abelian integral,the smaller upper bound for number of isolated zeros of Abelian integral is obtained through multiple derivative for reducing its order.The obtained conclusion improves the results of related literature.

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

分 类 号：O175[理学—数学]