| 一类Hamiltion系统的Abel积分的零点个数估计 |
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| 作者姓名： | SONG Yan |
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| 作者单位： | Department of Mathematics，Bohai University，Jinzhou 121000，China |
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| 摘 要： | In this paper, we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the system inside the class of all polynomial systems of degree n. The main result is that the upper bound for the number of zeros of the Abelian integral associated to this system is 3n-1.
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| 关 键 词： | 汉密尔顿系统 阿贝尔积分 皮卡德-傅克斯函数 一般洛尔定理 摄动微分多项式 |
The Estimation of the Number of Zeros of the Abelian Integrals for a Class of Hamiltonian Systems |
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| SONG Yan.The Estimation of the Number of Zeros of the Abelian Integrals for a Class of Hamiltonian Systems[J].Chinese Quarterly Journal of Mathematics,2005,20(2):158-162. |
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| Authors: | SONGYan |
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| Institution: | DepartmentofMathematics,BohaiUniversity,Jinzhou121000,China |
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| Abstract: | In this paper, we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the system inside the class of all polynomial systems of degree n. The main result is that the upper bound for the number of zeros of the Abelian integral associated to this system is 3n-1. |
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| Keywords: | Hamiltonian system Abelian integral Picard-Puchs equation general Rolle's theorem |
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