Abstract
This paper describes the use of the symbolic manipulation system MACSYMA to facilitate normal form and center manifold computations, which arise in nonlinear dynamics problems. These computations represent a relatively new approach towards obtaining approximate solutions to systems of ordinary differential equations. A near-identity coordinate transformation in the form of a power series is used to locally transform a given system into a normal (i.e., simple or canonical) form. Center manifold calculations are a related technique for reducing the number of dimensions in a given system of ordinary differential equations by restricting attention to the flow on an invariant subspace. A MACSYMA program developed to perform such computations is presented and described in detail. The program is illustrated by applying it to a sample nonlinear dynamics problem.
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