Normal Forms of Planar Polynomial Differential Systems

被引：0
|
作者：
Abderrahmane Turqui
Dahira Dali
机构：
[1] University of Sciences and Technology Houari Boumediene,Faculty of Mathematics
来源：
Qualitative Theory of Dynamical Systems | 2019年 / 18卷
关键词：
Polynomial differential system; Invariant; Linear transformation; Normal form; 34C20; 14L36; 34G14; 15A72;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Using the invariant theory, we develop an algorithmic method, which is based on the construction of a matrix of linear transformation, to compute normal forms of planar polynomial differential systems. We illustrate our method in the case where the planar polynomial differential system is cubic.
引用
收藏
页码：11 / 33
页数：22
相关论文
共 50 条
  • [41] Darboux invariants for planar polynomial differential systems having an invariant conic
    Llibre, Jaume
    Messias, Marcelo
    Reinol, Alisson C.
    [J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2014, 65 (06): : 1127 - 1136
  • [42] On the Singularities of the Planar Cubic Polynomial Differential Systems and the Euler Jacobi Formula
    Llibre, Jaume
    Valls, Claudia
    [J]. QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2020, 19 (03)
  • [43] On the center criterion of planar quasi-homogeneous polynomial differential systems
    Zhang, Liwei
    Yu, Jiang
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2018, 147 : 7 - 25
  • [44] Analytic integrability of cubic-linear planar polynomial differential systems
    Gine, Jaume
    Valls, Claudia
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (02) : 1690 - 1716
  • [45] Truncated normal forms for solving polynomial systems: Generalized and efficient algorithms
    Mourrain, Bernard
    Telen, Simon
    Van Barel, Marc
    [J]. JOURNAL OF SYMBOLIC COMPUTATION, 2021, 102 : 63 - 85
  • [46] Chaotification of polynomial continuous-time systems and rational normal forms
    Starkov, K
    Chen, GR
    [J]. CHAOS SOLITONS & FRACTALS, 2004, 22 (04) : 849 - 856
  • [47] POLYNOMIAL FIRST INTEGRALS FOR WEIGHT-HOMOGENEOUS PLANAR POLYNOMIAL DIFFERENTIAL SYSTEMS OF WEIGHT DEGREE 4
    Llibre, Jaume
    Valls, Claudia
    [J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2016, 46 (05) : 1619 - 1642
  • [48] Polynomial first integrals for weight-homogeneous planar polynomial differential systems of weight degree 3
    Cairo, Laurent
    Llibre, Jaume
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 331 (02) : 1284 - 1298
  • [49] Normal forms for general polynomial matrices
    Beckermann, Bernhard
    Labahn, George
    Villard, Gilles
    [J]. JOURNAL OF SYMBOLIC COMPUTATION, 2006, 41 (06) : 708 - 737
  • [50] Shifted normal forms of polynomial matrices
    Beckermann, B
    Labahn, G
    Villard, G
    [J]. ISSAC 99: PROCEEDINGS OF THE 1999 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, 1999, : 189 - 196
12345