| 一类二次可逆系统的Abel积分 |
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| 引用本文： | 洪晓春. 一类二次可逆系统的Abel积分[J]. 数学的实践与认识, 2010, 40(3) |
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| 作者姓名： | 洪晓春 |
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| 作者单位： | 曲靖师范学院数学与信息科学学院,云南曲靖655011;曲靖师范学院应用数学研究所,云南曲靖655011 |
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| 基金项目： | 云南省自然科学基金(2005A0080M,2008ZC153M) |
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| 摘 要： | 利用Picard-Fuchs方程法及Riccati方程法,研究了一类二次可逆系统在任意n次多项式扰动下Abel积分零点个数的上界问题,得到了当n≥4时,上界为10n+[n/2]-1.
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| 关 键 词： | 二次可逆系统 Able积分 Picard-Fuchs方程 Riccati方程 |
Abelian Integrals for a Class of Quadratic Reversible System |
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| HONG Xiao-Chun. Abelian Integrals for a Class of Quadratic Reversible System[J]. Mathematics in Practice and Theory, 2010, 40(3) |
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| Authors: | HONG Xiao-Chun |
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| Affiliation: | HONG Xiao-Chun (1.School of Mathematics , Information Science Qujing Normal College,Qujing 655011,China) (2.Institute of Applied Mathematics Qujing Normal College,China) |
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| Abstract: | By using the method of Picard-Fuchs equation and the Riccati equation method, we give an upper bound on the number of zeros of Abelian integrals for the quadratic reversible system under polynomial perturbations of arbitrary degree n.The upper bound is 10n +[n/2]- 1 when n≥4. |
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| Keywords: | quadratic reversible system Abelian integral Picard-Fuchs equation Riccati equation |
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