Journal of Jilin University Science Edition

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Nonintegrability of Differential Systems Based onCentral Manifolds Theory

JIAO Jia1, ZHOU Qingjian1,2, ZHOU Ran3   

  1. 1. College of Science, Dalian Nationalities University, Dalian 116600, Liaoning Province, China;2. Faculty of Management and Economics, Dalian University of Technology, Dalian 116024, Liaoning Province, China; 3. College of Mathematics, Jilin University, Changchun 130012, China
  • Received:2013-05-02 Online:2014-03-26 Published:2014-03-20
  • Contact: ZHOU Qingjian E-mail:zqj68@dlnu.edu.cn

Abstract:

We investigated the nonintegrability of differential systems by center manifolds theory. For the particular system with zero eigenvalues, we obtained a new criteria with nonexistence of nontrivial formal first integrals. An application was given at last to illustrate our statements.

Key words:  central manifold theory, first integral, Kowalevskaya matrix

CLC Number: 

  • O175.14