Algebraic features of some computational problems in nonlinear stability theory

Recently, a computational algorithm was developed to estimate the domain of attraction of smooth nonlinear ordinary differential equations. The algorithm is based on the approximation of the solutions of such equations by those of a Carleman linearization of the system as suggested in the work of Krener and Brockett. Preliminary applications of the algorithm to second order systems have been encouraging. Applications to more complex systems raise some interesting al gebraic questions in relation to the implementation of the algorithm. Our presentation will focus on these issues.