SINGULARITY STRUCTURE OF 3RD-ORDER DYNAMICAL-SYSTEMS .1.

A general third-order dynamical system with polynomial right-hand side s of finite degrees in the dependent variables is analyzed to unravel the singularity structure of its solutions about a movable singular po int, To that end, the system is first transformed to a second-order Br iot-Bouquet system and a third auxiliary equation via a transformation , similar to one used earlier by R. A. Smith in 1973-1974 for a genera l second-order dynamical system. This transformation imposes some cons traints on the coefficients appearing in the general third-order syste m. The known results for the second-order Briot-Bouquet system are use d to explicitly write out Laurent or psi-series solutions of the gener al third-order system about a movable singularity. The convergence of the relevant series solutions in a deleted neighborhood of the singula rity is ensured, The theory developed here is illustrated with the hel p of the May-Leonard system.