A MAPLE PROGRAM FOR THE GENERATION OF THE LIE-SERIES SOLUTION OF SYSTEMS OF NONLINEAR ORDINARY DIFFERENTIAL-EQUATIONS

The Lie series is a power series in which the initial conditions are part of the constant coefficients of the series. This property makes the Lie series appropriate for the study of systems of differential equations that exhibit chaotic behavior and, therefore, are sensitive to initial conditions. We present the theory behind the Lie series, a MAPLE program capable of handling single as well as systems of ODE's, several examples of the application of the program to linear and non-linear problems, and a discussion of the application to chaotic systems.