Poincare' normal forms and simple compact Lie groups

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.

arXiv comment17 pages; minor corrections in revised version

References in corpus (1)

• Convergence of normal form transformations: The role of symmetries

Cited by in corpus (1)

• Geometry of Normal Forms for Dynamical Systems