Giuseppe Gaeta
Poincare' normal forms and simple compact Lie groups
(52K, LaTeX)

ABSTRACT.  We classify the possible behaviour of 
Poincar\'e-Dulac normal forms for dynamical systems in $R^n$ with 
nonvanishing linear part and which are equivariant under 
(the fundamental representation of) all the simple compact 
Lie algebras and thus the corresponding simple compact Lie groups. 
The ``renormalized forms'' of these systems is also discussed; 
in this way we are able to 
simplify the classification and moreover to analyze systems with 
zero linear part. We also briefly discuss the convergence of the 
normalizing transformations. 
[This is an updated version of preprint MP-ARC 99-317]