Non-existence criteria for Laurent polynomial first integrals

S. Shi, Jilin University, Changchun, P. R. China
Y. Han, Jilin University, Changchun, P. R. China

E. J. Qualitative Theory of Diff. Equ., No. 6. (2003), pp. 1-11.

Communicated by Bo Zhang. Appeared on 2003-01-01

Abstract: In this paper we derived some simple criteria for non-existence and partial non-existence Laurent polynomial first integrals for a general nonlinear systems of ordinary differential equations $\dot x = f(x)$, $x \in R^n$ with $f(0) = 0$. We show that if the eigenvalues of the Jacobi matrix of the vector field $f(x)$ are $Z$-independent, then the system has no nontrivial Laurent polynomial integrals.

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