Poincare' normal forms and simple compact Lie groups

Details Poincare' normal forms and simple compact Lie groups Poincare' normal forms and simple compact Lie groups

2001-06-19

arxiv.org/abs/math-ph/0106016v2

Int. J. Mod. Phys. A 17 (2002), 3571-3587

Physics

Mathematical Physics

17 pages; minor corrections in revised version

Scientific paper

10.1142/S0217751X02011382

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'' (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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