中文摘要：

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．

英文摘要：

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.