ON TRANSFORMATIONS INTO NORMAL-FORM

We discuss a certain class of transformations of an ordinary differential equation into normal form near a stationary point. These transformations preserve certain special structures and one can derive from them a universally applicable algorithm to determine a normal form up to any desired degree. The algorithm can be programmed with the help of any computer algebra system. In the same manner, transformations into normal form on an invariant manifold are discussed. © 1993 Academic Press, Inc.