On analytic insolubility of the stability problem on the plane

被引：4

作者：

Medvedeva, N. B. ^{[1
]}

机构：

[1] Chelyabinsk State Univ, Chelyabinsk, Russia

来源：

RUSSIAN MATHEMATICAL SURVEYS | 2013年 / 68卷 / 05期

基金：

俄罗斯基础研究基金会;

关键词：

vector field; monodromic singular point; focus; centre; monodromy transformation; Newton diagram; blow-up of singularities; MONODROMY TRANSFORMATION;

D O I：

10.1070/RM2013v068n05ABEH004861

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This is a survey on questions involving algebraic and analytic solubility of the problem of stability of a singular point of a vector field on the plane, and in particular of the problem of distinguishing between a centre and a focus. It is proved that the stability problem on the plane is analytically insoluble.

引用

页码：923 / 949

页数：27

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