| 二阶多项式系统固定奇点附近解的解析展开 |
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| 引用本文： | 雷锦志,管克英.二阶多项式系统固定奇点附近解的解析展开[J].数学年刊A辑(中文版),2001(5). |
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| 作者姓名： | 雷锦志 管克英 |
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| 作者单位： | 北京航空航天大学数学系 北京100083
(雷锦志)，北方交通大学数学系 北京(管克英) |
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| 摘 要： | 研究二阶多项式系统所确定的通过固定奇点的解．利用牛顿图法研究了这种解在固定奇点处的幂级数展开式，给出有无穷多个解通过固定奇点的判据，并在只有有限个解通过固定奇点的情况下，给出了过固定奇点的解个数的上界．
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| 关 键 词： | 多项式系统 固定奇点 代数解 |
ANALYTIC EXPANSION OF SOLUTION PASSING SINGULAR POINT OF SECOND ORDER POLYNOMIAL SYSTEM |
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| LEI Jinzhi,GUAN Keying.ANALYTIC EXPANSION OF SOLUTION PASSING SINGULAR POINT OF SECOND ORDER POLYNOMIAL SYSTEM[J].Chinese Annals of Mathematics,2001(5). |
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| Authors: | LEI Jinzhi GUAN Keying |
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| Institution: | LEI Jinzhi,GUAN Keying Department of Mathematics,Beijing University of Aeronautics and Astronautics,Beijing 100083,China. E-mail: jzhlei@263.net Department of Mathematics,Northern Jiaotong University,Beijing 100044,China. |
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| Abstract: | Solutions passing the singular points of second order polynomial system are studied. Expand the solutions near the singular point by using the method presented by Newton while studying algebraic function. Through the method, a criterion of whether there are infinite solutions passing the singular point is given, and while not the case) an upper-bound of such solutions is also given. |
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| Keywords: | Polynomial system Fix singular point Algebraic solution |
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