G. Gaeta
Algorithmic reduction of Poincare'-Dulac normal forms and
Lie algebraic structure
(259K, PostScript)
ABSTRACT. The Poincare'-Dulac normal form of a given resonant system is in
general non unique; one would thus like, given a specific normal form,
to further reduce it to a simplest normal form. In this note we give
an algorithm, based on the Lie algebraic structure of the set of
normal forms, to obtain this. The algorithm proposed here can be
applied only under some condition, non generic but often met in
applications. When applicable, it only requires to solve linear
equations.