| 一类时间可逆系统的首次积分问题 |
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| 引用本文： | 桑波,刘文健,朱思铭.一类时间可逆系统的首次积分问题[J].天津师范大学学报(自然科学版),2011,31(2):9-11. |
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| 作者姓名： | 桑波 刘文健 朱思铭 |
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| 作者单位： | 1. 聊城大学,数学科学学院,山东,聊城,252059
2. 中山大学,数学与计算科学学院.广州,510275 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 对于一类时间可逆解析系统建立了首次积分的系数递推公式.利用此递推公式得到其具有给定形式首次积分的充要条件.为了说明所得结论,对于一类时间可逆三次系统,利用系数递推公式给出了其六次多项式首次积分.
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| 关 键 词： | 时间可逆系统 三次系统 首次积分 Darboux多项式 |
First integral problem for a class of time-reversible systems |
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| SANG Bo,LIU Wenjian,ZHU Siming.First integral problem for a class of time-reversible systems[J].Journal of Tianjin Normal University(Natural Science Edition),2011,31(2):9-11. |
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| Authors: | SANG Bo LIU Wenjian ZHU Siming |
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| Institution: | SANG Bo1,LIU Wenjian1,ZHU Siming2 1.College of Mathematics Science,Liaocheng University,Liaocheng 252059,Shandong Province,China,2.College of Mathematics and Computational Science,Sun Yat-Sen University,Guangzhou 510275 |
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| Abstract: | For a class of time-reversible analytic systems,coefficients' recurrence formulae of first integral are obtained,by which some necessary and sufficient conditions for the systems to have prescribed first integral are reached.To illustrate the results,six degree polynomial first integral of a cubic time-reversible system is obtained by the coefficients' recurrence formulae. |
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| Keywords: | time-reversible systems cubic systems first integral Darboux polynomial |
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