| 复自治微分系统(E)的奇点量计算公式 |
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| 引用本文： | 时宝. 复自治微分系统(E)的奇点量计算公式[J]. 海军工程大学学报, 1991, 0(4) |
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| 作者姓名： | 时宝 |
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| 作者单位： | 海军航空工程学院 |
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| 摘 要： | 文献[1]对(E)引入奇点量和 Lie 不变量概念,实现了实自治微分系统焦点量和鞍点量概念的统一,并得到奇点量的结构定理。文献[1]还对三次系统(E_3)找到了全部120个基本 Lie 不变量并具体计算了二次系统(E_2)和缺二次项的三次系统(E_3~((3)))的奇点量。文献[2]还计算了一类特殊三次系统(4)的奇点量。但是,对于计算(E_3)的奇点量的工作,仍有很大困难,甚至前几个奇点量也得不到,况且对(E)找到全部基本Lie 不变量亦非常困难。本文利用规范形理论讨论(E)的奇点量的计算问题,得到了计算公式。该公式对一些特殊系统可直接得到前几个奇点量。作为公式的应用及验证,我们给出(E_3)的前两个奇点量,至于 M(3)=?的问题将另文讨论。
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| 关 键 词： | 微分系统 奇点量 规范形 |
Computational Formula of Singular Values of Complex Autonomous Differential Systems |
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| Shi Bao. Computational Formula of Singular Values of Complex Autonomous Differential Systems[J]. Journal of Naval University of Engineering, 1991, 0(4) |
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| Authors: | Shi Bao |
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| Abstract: | Reference [1] defined two concepts of singular values for complex autonomous differential sys- tems (ADS) and Lie invariants,the former united the concepts of focal values and saddle values in real ADS and the latter gave a structure theorem,with which the singular values of (E_2),(E_2~(?)) and a giv- en class of cubic system discussed in reference [2] were computed.But,it is still difficult to compute sigular values.In this paper,the author applies the normal form theory to the computation of singular values of complex ADS,and gets a formula of computing singular values,which is more simple to use. By the formula,we can directly get teh first singular values for some given classes of systems. |
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| Keywords: | Differential system Singular values Normal form |
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