REDUCTION OF POINCARE NORMAL FORMS

摘要

The Poincare algorithm for reducing a system of ODEs to normal form (near an equilibrium point) is based on considering near-identity changes of coordinates generated by homogeneous polynomial functions h(k). These are chosen in such a way as to eliminate the nonresonant terms of a corresponding order. We show that careful consideration of the higher-order terms generated in the transformation, and use of the arbitrarily in the choice of h(k), permit us to obtain a significant simplification of the normal form. Our results are illustrated by a relevant example. [References: 17]