Tracing phase portraits of planar polynomial vector fields with detailed analysis of the singularities

被引：0

作者：

Dumortier F. ^{[1
]}

Herssens C. ^{[1
]}

机构：

[1] Limburgs Universitair Centrum, Universitaire Campus

来源：

Qualitative Theory of Dynamical Systems | 1999年 / 1卷 / 1期

关键词：

blow-up; Newton-diagram; ordinary differential equation; phase portrait; singularity; vector field;

D O I：

10.1007/BF02969406

中图分类号：

学科分类号：

摘要：

The paper essentially aims at presenting a computer program drawing phase portraits of planar polynomial vector fields. It is essentially based on a detailed analysis of the singularities by means of desingularization using quasihomogeneous blow-up and the Newton diagram, and good approximation of invariant manifolds. Phase portraits can be drawn locally near a singularity or globally on a Poincaré disc or a Poincaré-Lyapunov disc, compactifying the plane. © 1999 Birkhäuser-Verlag.

引用

页码：97 / 130

页数：33

共 14 条

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