Electron. J. Differential Equations, Vol. 2017 (2017), No. 274, pp. 1-11.

Higher order criterion for the nonexistence of formal first integral for nonlinear systems

Zhiguo Xu, Wenlei Li, Shaoyun Shi

Abstract:
The main purpose of this article is to find a criterion for the nonexistence of formal first integrals for nonlinear systems under general resonance. An algorithm illustrates an application to a class of generalized Lokta-Volterra systems. Our result generalize the classical Poincare's nonintegrability theorem and the existing results in the literature.

Submitted April 13 2016. Published November 5, 2017.
Math Subject Classifications: 34C14, 34M25.
Key Words: Normal form theory; first integral; resonance.

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Zhiguo Xu
School of Mathematics, Jilin University
Changchun 130012, China
email: xuzg2014@jlu.edu.cn
Wenlei Li
School of Mathematics, Jilin University
Changchun 130012, China
email: lwlei@jlu.edu.cn
phone: +86-431-85166042
Shaoyun Shi
School of Mathematics &
State key laboratory of automotive simulation and control
Changchun 130012, China
email: shisy@jlu.edu.cn

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