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
收藏
页码：97 / 130
页数：33
相关论文
共 50 条
  • [21] Simple Darboux points of polynomial planar vector fields
    Ollagnier, JM
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2004, 189 (1-3) : 247 - 262
  • [22] Periodic perturbations of quadratic planar polynomial vector fields
    Messias, M
    ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS, 2002, 74 (02): : 193 - 198
  • [23] On planar polynomial vector fields with elementary first integrals
    Christopher, Colin
    Llibre, Jaume
    Pantazi, Chara
    Walcher, Sebastian
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 267 (08) : 4572 - 4588
  • [24] The linear term of the Poincaré map at singularities of planar vector fields
    Garcia, Isaac A.
    Gine, Jaume
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 396 : 44 - 67
  • [25] Weak Singularities of Planar Vector Fields Under Weak Perturbation
    Douglas S. Shafer
    Journal of Dynamics and Differential Equations, 2004, 16 (1) : 65 - 90
  • [26] Realization problems for limit cycles of planar polynomial vector fields
    Margalef-Bentabol, Juan
    Peralta-Salas, Daniel
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (04) : 3844 - 3859
  • [27] Commuting planar polynomial vector fields for conservative Newton systems
    Nagloo, Joel
    Ovchinnikov, Alexey
    Thompson, Peter
    ACM COMMUNICATIONS IN COMPUTER ALGEBRA, 2018, 52 (03): : 59 - 62
  • [28] Commuting planar polynomial vector fields for conservative Newton systems
    Nagloo, Joel
    Ovchinnikov, Alexey
    Thompson, Peter
    COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2020, 22 (04)
  • [29] The Bifurcation of the Equatorial Periodic Orbit of the Planar Polynomial Vector Fields
    Xin An Zhang
    Lan Sun Chen
    Zhao Jun Liang
    Acta Mathematica Sinica, 2001, 17 : 471 - 480
  • [30] The bifurcation of the equatorial periodic orbit of the planar polynomial vector fields
    Zhang, XA
    Chen, LS
    Liang, ZJ
    ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2001, 17 (03) : 471 - 480
12345