POINCARÉ NORMAL FORMS AND SIMPLE COMPACT LIE GROUPS

We classify the possible behavior of Poincaré–Dulac normal forms for dynamical systems in Rⁿ 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" (in the sense of Ref. 22) 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.