 96263 G. Gaeta
 Poincare' renormalized forms
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Jun 13, 96

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Abstract. In Poincar\'e Normal Form theory, one considers a series
of transformations generated by homogeneous polynomials obtained as
solution of the homological equation; such solutions are unique up to
terms in the kernel of the homological operator. Careful consideration
of the higher order terms generated by polynomials differing for a term
in this kernel leads to the possibility of further reducing the Normal
Form expansion of a formal power series, in a completely algorithmic way.
The algorithm is also applied to planar vector fields whose linear part
has eigenvalues $\la = \pm i$.
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