On the normal form of a system of differential equations with nilpotent linear part

被引：4

作者：

Canalis-Durand, M ^{[1
]}

Schäfke, R

机构：

[1] Univ Aix Marseille 3, GREQAM, F-13002 Marseille, France

[2] Univ Strasbourg 1, IRMA, F-67084 Strasbourg, France

来源：

COMPTES RENDUS MATHEMATIQUE | 2003年 / 336卷 / 02期

关键词：

D O I：

10.1016/S1631-073X(02)00022-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider prenormal forms associated to generic perturbations of the system (x) over dot = 2y, (y) over dot 3x(2). It is known that they have a formal normal form (x) over dot = 2y + 2x Delta*, (y) over dot = 3x(2) + 3y Delta*, where Delta* = x + A(0)(y(2) - x(3)) [Differential Equations 158 (1) (1999) 152-173]. We show that the series A0 and the normalizing transformations are divergent, but 1-summable.

引用

页码：129 / 134

页数：6

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