Strong nilpotence holds in dimensions up to five only
Strong nilpotence holds in dimensions up to five only
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DOI：
10.1080/03081089108818109
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发表时间：
1991-11
影响因子：
1.1
通讯作者：
G. Meisters;C. Olech
中科院分区：
文献类型：
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作者：
G. Meisters;C. Olech
首先证明了2次齐次多项式映射的幂零雅可比矩阵Q1(X)在n-因子乘积为零的意义下是强幂零的，并给出了5维上的一些反例(由于VI.Vasyunin)。然后，对于n维5的这些情形以及任意维n的几种情形，利用该公式明确地给出了(必然可逆)二次映射F(X)=x−q(X)的逆是Wazewski微分方程解(显式得到的).
First it is proved, in dimensions n < 5, that nilpotent Jacobian matrices Q1(x) of homogeneous degree 2 polynomial maps are strongly nilpotent in the sense that arbitrary n-factor products are zero; and some counterexamples to this in dimension 5 (due to V I. Vasyunin) are given. Then, for these cases in dimensions n 5 as well as for several cases in arbitrary dimension n, the inverse of the (necessarily invertible) quadratic map F(x)= x − Q(x) is given explicitly by making use of the formula is the (explicitly obtained) solution of the Wazewski Differential Equation .