一类五次扰动Hamiltonian系统的Abel积分零点个数  

The Number of Zeros of Abelian Integral for Some Perturbed Hamiltonian System of Degree 5

作　　者：孙宪波[1] 

机构地区：[1]广西财经学院信息与统计学院应用数学系,南宁530003

出　　处：《数学学报（中文版）》2013年第6期981-992,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11261013);广西财经学院校级科研项目(2012C08);广西高校科研项目(2013YB216)

摘　　要：研究一类五次扰动Hamiltonian系统的Abel积分零点个数上界.证明所研究的Abel积分的生成元构成精度为1的Chebeyshev系统,得到Abel积分零点个数上界是4(考虑零点重数).并指出前人文献中关于Abel积分零点个数上界的研究存在的错误,给出了最新结果.We study the number of zeros of the Abelian integral for some perturbed Hamiltonian system of degree 5. We prove the generating elements of the Abelian integral form a Chebeyshev system of accuracy of 1, therefore the number of zeros of the Abelian integral is 4. Last, we show a wrong result given in some previous work about the number of zeros for this Abelian integral, therefore the result we give is very new.

关 键 词：ABEL积分 Chebeyshev系统 弱化Hilbert 16th问题 

分 类 号：O175.12[理学—数学]