INVARIANT ALGEBRAIC SURFACES OF SOME DYNAMICAL SYSTEM
Tinghua L(Dept. of Math., Shandong Institute of Business and Technology, Yantai 264005, Shandong)
In this paper, we study the invariant algebraic surfaces of a system, which generalizes the Lorenz system. Using the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations, we characterize all the Darboux invariants, the irreducible Darboux polynomials, the rational first integrals and the algebraic integrability of this system.