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Nonexistence of formal first integrals for general nonlinear systems under resonance
Fang Liu,Shaoyun Shi *,Zhiguo Xu
College of Mathematics, Jilin University
*Correspondence author
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Funding: 教育部博士点基金,国家自然科学基金（No.20040183030,10771083）
Opened online:19 December 2007
Accepted by: none
Citation: Fang Liu,Shaoyun Shi,Zhiguo Xu.Nonexistence of formal first integrals for general nonlinear systems under resonance[OL]. [19 December 2007] http://en.paper.edu.cn/en_releasepaper/content/17140
 
 
In the present paper, we consider the non-integrability for nonlinear system under the simple resonant case, i.e., the Jacobian matrix of vector field at some fixed point has some single multiply zero eigenvalues, and some nonzero eigenvalues which are $\\\\\\\\\\\\\\\\mathbb{N}$-independent. By using normal form theory, we give a necessary condition for this kind of system to have formal first integral.
Keywords:Nonexistence;Formal first integrals; Resonance
 
 
 

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