Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in C2

被引：38

作者：

Christopher, C ^{[1
]}

Rousseau, C

机构：

[1] Univ Plymouth, Sch Math & Stat, Plymouth PL4 8AA, Devon, England

[2] Univ Montreal, Dept Math & Stat, Montreal, PQ H3C 3J7, Canada

[3] Univ Montreal, CRM, Montreal, PQ H3C 3J7, Canada

来源：

PUBLICACIONS MATEMATIQUES | 2001年 / 45卷 / 01期

关键词：

D O I：

10.5565/PUBLMAT_45101_04

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper me consider complex differential systems in the plane, which are linearizable in the neighborhood of a nondegenerate centre. We find necessary and sufficient conditions for linearizability for the class of complex quadratic systems and for the class of complex cubic systems symmetric with respect to a centre. The sufficiency of these conditions is shown by exhibiting explicitly a linearizing change of coordinates, either of Darboux type or a generalization of it.

引用

页码：95 / 123

页数：29

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