96-584 G. Gaeta

Poincare' renormalized forms (77K, plain TeX) Nov 22, 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 a number of concrete cases. An alternative formulation, conceptually convenient but computationally unpractical, is also presented, and it is shown that the discussion immediately extends to the Hamiltonian case and Birkhoff normal forms. [This is a revised and much expanded version of MP-ARC 96-263]

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