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.