| 一类四次Hamilton函数Abel积分零点个数的估计 |
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| 引用本文： | 周鑫,李翠萍,张艳. 一类四次Hamilton函数Abel积分零点个数的估计[J]. 系统科学与数学, 2009, 29(3): 323-330 |
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| 作者姓名： | 周鑫 李翠萍 张艳 |
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| 作者单位： | 北京航空航天大学数学系数学、信息与行为教育部重点实验室,北京,100191 |
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| 摘 要： | 证明了Abel积分I(h)=∮ΓhQ(x,y)dx-P(x,y)dy的零点个数的最小上界B(2n+2)=B(2n+1)≤3[n/2]+12[(n-1)/2]+4([p]表示P的整数部分),这里n是代数曲线H(x,Y)=x2士x4+Y4=h的连通闭分支,h∈E(Γh存在的最大开区间),P(x,y),Q(x,Y)是关于x,y 的次数不超过2n+2或2n+1的实多项式.
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| 关 键 词： | Hamilton系统 Abel积分 Picard-Fuchs方程 |
| 收稿时间： | 2007-04-06 |
| 修稿时间： | 2007-10-19 |
Estimation of the Number of Zeros of Abelian Integral for a Kind of Quartic Hamiltonians |
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| ZHOU Xin,LI Cuiping,ZHANG Yan. Estimation of the Number of Zeros of Abelian Integral for a Kind of Quartic Hamiltonians[J]. Journal of Systems Science and Mathematical Sciences, 2009, 29(3): 323-330 |
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| Authors: | ZHOU Xin LI Cuiping ZHANG Yan |
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| Affiliation: | Department of Mathematics and LMIB, Beihang University, Beijing 100191 |
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| Abstract: | It is proved that the supremum of the number of zeros of Abelian integral I(h)=oint_{{it Gamma}_h}Q(x,y)dx-P(x,y)dy satisfies B(2n+2)=B(2n+1)leq3[frac{n}{2}]+12[frac{n-1}{2}]+4 ([p] denotes the entire part of p), where {Gamma}_h is a compact component of H(x,y)=x^2pm{x^4}+y^4=h, hin Sigma(a maximal open interval of {Gamma}_h),P(x,y),Q(x,y) are real polynomials of x,y with degree not greater than 2n+2 or 2n+1. |
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| Keywords: | Hamiltonian systems abelian integral picard-fuchs equations. |
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