01-16 G. Gaeta

On the integration of resonant Poincar\'e-Dulac normal forms (36K, LaTeX) Jan 11, 01

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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.

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