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.