On the Poincare problem

被引：39

作者：

Walcher, S ^{[1
]}

机构：

[1] Tech Univ Munich, Zentrum Mathemat, D-80290 Munich, Germany

[2] GSF Forschungszentrum, Inst Biomath & Biometrie, D-85764 Neuherberg, Germany

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2000年 / 166卷 / 01期

关键词：

D O I：

10.1006/jdeq.2000.3801

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We derive some restrictions an the possible degrees of algebraic invariant curves and on the possible Form of algebraic integrating factors, for plane polynomial vector fields whose stationary points at infinity satisfy a certain genericity condition. The method is elementary, and we show by example that it also yields strong results for certain non-generic vector fields. (C) 2000 Academic Press.

引用

页码：51 / 78

页数：28