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Poincare' normal forms and simple compact Lie groups

Giuseppe Gaeta
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Abstract

We classify the possible behaviour of Poincaré-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'' (in the sense of previous work by the author) 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.

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Giuseppe Gaeta. 2001-12-20. Poincare' normal forms and simple compact Lie groups. https://doi.org/10.1142/s0217751x02011382

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