| 一类单中心二次可积系统的Abel积分零点个数 |
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| 引用本文： | 张永康,李翠萍,李宝毅.一类单中心二次可积系统的Abel积分零点个数[J].系统科学与数学,2012,32(5):626-640. |
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| 作者姓名： | 张永康 李翠萍 李宝毅 |
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| 作者单位： | 1. 北京航空航天大学数学与系统科学学院数学,信息与行为教育部重点实验室,北京100191
2. 天津师范大学数学科学学院,天津,300387 |
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| 基金项目： | 国家自然科学基金重点项目，中央高校基本科研业务费专项资金资助课题 |
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| 摘 要： | 讨论了首次积分为H(x,y)=x~k(1/2y~2+Ax~2+Bx+C)的Abel积分的代数构造,并研究了k=2时具有一个中心的平面二次可积系统在n次扰动下的Abel积分零点个数上界问题,得到了较小的上界估计,
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| 关 键 词： | Abel积分 Picard-Fuchs方程 Riccati方程 |
THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR A CLASS OF PLANE QUDRATIC INTEGRABLE SYSTEMS WITH ONE CENTRE |
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| ZHANG Yongkang
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LI Cuiping
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LI Baoyi.THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR A CLASS OF PLANE QUDRATIC INTEGRABLE SYSTEMS WITH ONE CENTRE[J].Journal of Systems Science and Mathematical Sciences,2012,32(5):626-640. |
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| Authors: | ZHANG Yongkang LI Cuiping LI Baoyi |
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| Institution: | (School of Mathematical Sciences,Tianjin Normal University,Tianjin 300387) |
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| Abstract: | In this paper,we obtain the finite generators of Abelian integral I（h） =∮Γh（M（x,y）g（x,y））dx -（M（x,y）f（x,y））dy,whereΓh is a family of closed ovals defined by H（x,y） = xk（1/2y2 + Ax2 + Bx + C） = h,h∈E,k is a positive integer,E is the open interval on whichΓh is defined,f（x,y） and g（x,y） are real polynomials in x and y of degrees,not exceeding n.An upper bound of the number of zeros of Abelian integral I（h）,for the above system with one centre,is given by its algebraic structure for a special case. |
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| Keywords: | Abelian integrals Picard-Puchs equation Riccati equation |
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