 93132 Cicogna G., Gaeta G.
 Poincare' normal forms and Lie point symmetries
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May 13, 93

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Abstract. We study Poincare' normal forms of vector fields in the
presence of symmetry under general  i.e. not necessarily
linear  diffeomorphisms. We show that it is possible to
reduce both the vector field and the symmetry diffeomorphism
to normal form by mean of an algorithmic procedure similar
to the usual one for Poincare' normal forms without symmetry;
this 'double' normal form can be given a simple geometric
characterization.
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