 0118 Giuseppe Gaeta
 Poincare' normal forms and simple compact Lie groups
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Jan 11, 01

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Abstract. We classify the possible behaviour of
Poincar\'eDulac 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 MPARC 99317]
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