Unique Normal Form and the Associated Coefficients for a Class of Three-Dimensional Nilpotent Vector Fields

被引：3
作者：
Li, Jing [1 ]
Kou, Liying [1 ]
Wang, Duo [2 ]
机构：
[1] Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China
[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2017年 / 27卷 / 14期
基金：
北京市自然科学基金; 中国国家自然科学基金;
关键词：
Three-dimensional nilpotent vector field; unique normal form; multiple Lie bracket; transformation with parameters; REDUCTION;
D O I：
10.1142/S0218127417502248
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we mainly focus on the unique normal form for a class of three-dimensional vector fields via the method of transformation with parameters. A general explicit recursive formula is derived to compute the higher order normal form and the associated coefficients, which can be achieved easily by symbolic calculations. To illustrate the efficiency of the approach, a comparison of our result with others is also presented.
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页数：16
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共 17 条
  • [1] FURTHER REDUCTION OF THE TAKENS-BOGDANOV NORMAL-FORM
    BAIDER, A
    SANDERS, JA
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1992, 99 (02) : 205 - 244
  • [2] Chen GT, 1999, ISSAC 99: PROCEEDINGS OF THE 1999 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, P165, DOI 10.1145/309831.309900
  • [3] An algorithm for computing a new normal form for dynamical systems
    Chen, GT
    Della Dora, J
    [J]. JOURNAL OF SYMBOLIC COMPUTATION, 2000, 29 (03) : 393 - 418
  • [4] A SIMPLE GLOBAL CHARACTERIZATION FOR NORMAL FORMS OF SINGULAR VECTOR-FIELDS
    ELPHICK, C
    TIRAPEGUI, E
    BRACHET, ME
    COULLET, P
    IOOSS, G
    [J]. PHYSICA D, 1987, 29 (1-2): : 95 - 127
  • [5] A note on the triple-zero linear degeneracy:: Normal forms, dynamical and bifurcation behaviors of an unfolding
    Freire, E
    Gamero, E
    Rodríguez-Luis, AJ
    Algaba, A
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2002, 12 (12): : 2799 - 2820
  • [6] Hypernormal form calculation for triple-zero degeneracies
    Gamero, E
    Freire, E
    Rodríguez-Luis, AJ
    Ponce, E
    Algaba, A
    [J]. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 1999, 6 (03) : 357 - 368
  • [7] Linear grading function and further reduction of normal forms
    Kokubu, H
    Oka, H
    Wang, D
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 132 (02) : 293 - 318
  • [8] Li J, 2001, DYNAM CONT DIS SER A, V8, P519
  • [9] Li J, 2017, INT J BIFURCAT CHAOS, V27
  • [10] Unique normal form of a class of 3 dimensional vector fields with symmetries
    Li, Jing
    Zhang, Lina
    Wang, Duo
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (07) : 2341 - 2359
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