94-68 Cicogna G., Gaeta G.

Normal forms and nonlinear symmetries (25K, TeX) Mar 24, 94

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Abstract. We give some general theorems, and extensions of previous results, concerning the problem of transforming an algebra of vector fields into Poincar\'e normal form. By means of an unifying algebraic language, we show the possibility of obtaining either a "parallel" or "joint" normal form of the vector fields in a well definite way, which simplifies the construction of normal forms, providing a precise restriction on their structure. The application to the finite dimensional dynamical systems and to their Lie point symmetries is also discussed.

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