ELA, Volume 8, pp. 14-25, February 2001, abstract.

Algebraic Curve Solution for Second-Order
Polynomial Autonomous Systems

Zhaosheng Feng

In this paper, by the method of the analysis of algebraic 
curves and the division theorem for two complex variables, 
the nonexistence of the algebraic curve solution of the 
second-order polynomial autonomous systems in the complex 
plane is obtained. The results are of important significance 
in the qualitative theory of polynomial autonomous systems 
and the integrability of nonlinear ordinary differential 
equations.