On the nonexistence of rational first integrals for nonlinear systems and semiquasihomogeneous systems

被引：20
作者：
Shi, Shaoyun [1 ]
机构：
[1] Jilin Univ, Coll Math, Changchun 130012, Peoples R China
[2] Jilin Univ, Minist Educ, Key Lab Symbol Computat & Knowledge Engn, Changchun 130012, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 335卷 / 01期
基金：
中国国家自然科学基金; 高等学校博士学科点专项科研基金;
关键词：
first integrals; Kowalevsky matrix; semiquasihomogeneous systems;
D O I：
10.1016/j.jmaa.2007.01.060
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we first give a necessary condition for general nonlinear systems to have rational first integrals. Then by using the so-called Kowalevsky exponents we present a criterion for nonexistence of rational first integrals for semiquasihomogeneous systems. (C) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码：125 / 134
页数：10
相关论文
共 14 条
[1]   On non-integrability of general systems of differential equations [J].
Furta, SD .
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1996, 47 (01) :112-131
[2]   Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations [J].
Goriely, A .
JOURNAL OF MATHEMATICAL PHYSICS, 1996, 37 (04) :1871-1893
[3]   Partial integrability for general nonlinear systems [J].
Kwek, KH ;
Li, Y ;
Shi, SY .
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2003, 54 (01) :26-47
[4]   Local first integrals of differential systems and diffeomorphisms [J].
Li, WG ;
Llibre, J ;
Zhang, X .
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2003, 54 (02) :235-255
[5]  
MOULINOLLAGNIER J, 1995, B SCI MATH, V119, P195
[6]   On the nonexistence of rational first integrals for systems of linear differential equations [J].
Nowicki, A .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1996, 235 :107-120
[7]   LIE SYMMETRIES OF THE LORENZ MODEL [J].
SEN, T ;
TABOR, M .
PHYSICA D, 1990, 44 (03) :313-339
[8]   Non-existence of first integrals in a Laurent polynomial ring for general semi-quasihomogeneous systems [J].
Shi, Shaoyun ;
Zhu, Wenzhuang ;
Liu, Baifeng .
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2006, 57 (05) :723-732
[9]   Non-integrability for general nonlinear systems [J].
Shi, SY ;
Li, Y .
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2001, 52 (02) :191-200
[10]  
SHI SY, 2003, ELECT J QUAL THEORY, P1
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