Further reduction of normal forms for vector fields

被引：15

作者：

Chen, GT ^{[1
]}

机构：

[1] Univ Lille 1, UFR Math, AGAT UMR 8524, F-59655 Villeneuve Dascq, France

来源：

NUMERICAL ALGORITHMS | 2001年 / 27卷 / 01期

关键词：

normal form; Lie's method; further reduction; vector field; dynamical system;

D O I：

10.1023/A:1016693005645

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Nye study Lie's method in the way of Ushiki for further reduction of normal forms for vector fields with singularity at the origin. We give further reduction of normal forms in two typical cases for vector fields in dimension 2: one with a rotation as its linear part and the other with a nilpotent linear part.

引用

页码：1 / 33

页数：33

共 28 条

[1]

Abraham R., 1988, APPL MATH SCI, V75

[2]

Arnold V. I., 1983, GEOMETRICAL METHODS

[3] FURTHER REDUCTION OF THE TAKENS-BOGDANOV NORMAL-FORM [J].

BAIDER, A ;

SANDERS, JA .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1992, 99 (02) :205-244

[4] UNIQUE NORMAL FORMS FOR VECTOR-FIELDS AND HAMILTONIANS [J].

BAIDER, A .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1989, 78 (01) :33-52

[5]

Bogdanov R. I., 1976, FUNCT ANAL APPL, V10, P61

[6]

Bruno A. D., 1979, LOCAL METHOD NONLINE

[7]

CHEN G, 1999, PUB IRMA LILLE, V50

[8] Further reductions of normal forms for dynamical systems [J].

Chen, GT ;

Della Dora, J .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 166 (01) :79-106

[9]

Chen GT, 1999, ISSAC 99: PROCEEDINGS OF THE 1999 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, P165, DOI 10.1145/309831.309900

[10] An algorithm for computing a new normal form for dynamical systems [J].

Chen, GT ;

Della Dora, J .

JOURNAL OF SYMBOLIC COMPUTATION, 2000, 29 (03) :393-418

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