Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2

被引：27

作者：

Cairo, Laurent

Llibre, Jaurne ^{[1
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

[2] Univ Orleans, MAPMO CNRS, Dept Math, F-45067 Orleans 2, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2007年 / 67卷 / 02期

关键词：

quadratic vector fields; integrability; rational first integral; phase portraits;

D O I：

10.1016/j.na.2006.04.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 2. In other words we characterize all the global phase portraits of the quadratic polynomial vector fields having all their orbits contained in conics. For such a vector field there are exactly 25 different global phase portraits in the Poincare disc, up to a reversal of sense. (c) 2006 Elsevier Ltd. All rights reserved.

引用

页码：327 / 348

页数：22

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