G. Gaeta
On the integration of resonant Poincar\'e-Dulac normal forms 
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ABSTRACT.  Given a nonlinear dynamical system in $\R^n$ in Poincar\'e-Dulac 
normal form, we associate to it an auxiliary linear system; solutions 
to the original system are obtained from solutions to the auxiliary 
one on a certain invariant submanifold, defined by resonance conditions. 
The auxiliary system is finite dimensional if the spectrum of the 
linearization of the original system satisfies only a finite number of 
resonance conditions, as implied e.g.by the Poincar\'e condition.