| 一类五次多项式系统无穷远点等时中心条件与极限环分支 |
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| 引用本文： | 王勤龙,刘一戎. 一类五次多项式系统无穷远点等时中心条件与极限环分支[J]. 高校应用数学学报(A辑), 2006, 21(2): 165-173 |
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| 作者姓名： | 王勤龙 刘一戎 |
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| 作者单位： | 中南大学,数学与计算技术学院,湖南,长沙,410083;长江大学,信息与数学学院,湖北,荆州,434100;中南大学,数学与计算技术学院,湖南,长沙,410083 |
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| 摘 要： | 研究一类五次系统无穷远点的中心、拟等时中心条件与极限环分支问题.首先通过同胚变换将系统无穷远点转化成原点,然后求出该原点的前8个奇点量,从而导出无穷远点成为中心和最高阶细焦点的条件,在此基础上给出了五次多项式系统在无穷远点分支出8个极限环的实例.同时通过一种最新算法求出无穷远点为中心时的周期常数,得到了拟等时中心的必要条件,并利用一些有效途径一一证明了条件的充分性.
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| 关 键 词： | 无穷远点 极限环分支 等时中心 五次系统 |
| 文章编号： | 1000-4424（2006）02-0165-09 |
| 收稿时间： | 2005-09-06 |
| 修稿时间： | 2005-09-06 |
Isochronous center conditions and limit cycles at infinity for a class of fifth systems |
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| WANG Qin-long,LIU Yi-rong. Isochronous center conditions and limit cycles at infinity for a class of fifth systems[J]. Applied Mathematics A Journal of Chinese Universities, 2006, 21(2): 165-173 |
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| Authors: | WANG Qin-long LIU Yi-rong |
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| Affiliation: | 1. Department of Mathematics ,Central South University ,Changsha 410083 .China 2. Department of Information and Mathematics ,Yangtze University ,dingzhou 434100 ,China |
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| Abstract: | In this article,the center conditions,isochronous center conditions and bifurcation of limit cycles at infinity for a class of fifth system are investigated.Firstly,the first eight singular point quantities are computed and conditions for infinity to be a center are deduced as well,then a system that bifurcates eight limit cycles in the neighborhood of infinity are constructed.At the same time the new algorithm is applied to find necessary conditions for such isochronous center,then proofs of isochronicity of these systems by using some effective methods are given. |
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| Keywords: | infinity bifurcation of limit cycle isochronous center fifth system |
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