**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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