Normal forms
Normal forms
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DOI：
10.1016/s0378-4754(97)00120-1
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发表时间：
1998-03
期刊：
影响因子：
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通讯作者：
A. D. Bruno
中科院分区：
文献类型：
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作者：
A. D. Bruno
考虑一个常微分方程组在其驻点附近的自治解。通过坐标的形式变换，我们可以将系统转化为它的规范形式。利用坐标的幂变换，将规范形问题化为一个维数较小的问题。在这里，我们比较两种标准形式：共振和Belitskii。我们讨论了它们的计算方法，并指出了一个新的性质，简化了计算的Belitskii标准形。我们应用这种方法来研究Henon-Heiles系统的周期解。
We consider an autonomous system of ordinary differential equations near its stationary point. By means of the formal change of coordinates, we can transform the system into its normal form. By means of the power transformation of coordinates, the normal form is reducd to a problem of less dimension. Here we compare two kinds of normal forms: resonant and Belitskii. We discuss methods of their computation and point out a new property which simplifies computation of the Belitskii normal form. We apply this approach to study periodic solutions of the Henon–Heiles system.