Locally finite and locally nilpotent derivations with applications to polynomial flows, morphisms and G_a-actions, II
Locally finite and locally nilpotent derivations with applications to polynomial flows, morphisms and G_a-actions, II
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局部有限和局部幂零推导及其在多项式流、态射和 G_a-actions 中的应用，II
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
A. Essen
中科院分区：
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作者：
A. Essen
引言在[13]中，我们试图推销以下口号“局部幂零和局部有限导子隐藏在许多问题中。然而，一旦它们的存在被揭示，关于这些推导的信息可以提供关于正在考虑的问题的有价值的信息。“为了说明这一说法，我们讨论了几个例子。利用局部有限导子和局部幂零导子的性质，我们给出了Lorenz方程和Maxwell-Bloch方程不具有多项式流的新的非常简单的证明（结果首先由Coomes在[7，8]中得到，Coomes和Rakkowski在[10]中得到）。也是二维多项式流的Bass-Meisters分类定理的一个很短的证明（参见[4])最后，我们描述了一个算法，以决定是否有两个
IntroductionIn [13] we tried to sell the following slogan "Locally nilpotent and locallyfinite derivations are hidden in many problems. However once their presence isrevealed, information on these derivations can give valuable information on theproblem under consideration." To illustrate that statement we discussed severalexamples. Using properties of locally finite and locally nilpotent derivations wegave new very simple proofs of the fact that the Lorenz equations and theMaxwell-Bloch equations do not have a polynomial flow (results first obtainedby Coomes in [7, 8] and Coomes and Zurkowski in [10]). Also a very short proofof the Bass-Meisters classification theorem of two dimensional polynomial flows(cf. [4]) was presented and finally we described an algorithm to decide if a two