TIME-INDEPENDENT INVARIANTS OF MOTION FOR THE QUADRATIC SYSTEM

A Hamiltonian method is developed to obtain first integrals of the for m PQ(mu) and P Q(mu) R(nu) for a general system of two-dimensional aut onomous ordinary differential equations with quadratic terms, where P, Q and R are linear or quadratic polynomials, and mu, nu are two real numbers. It is found that there is an intimate relationship between th e polynomials and the equilibrium points of the system, which is usefu l for determining the existence of periodic orbits and asymptotic beha viour.