G. Gaeta
Poincare' renormalized forms
(221K, gzipped PS)
ABSTRACT. In Poincare' 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 on the one side to the Hamiltonian case and Birkhoff normal
forms, and to the other to the equivariant setting.
This is a revised and expanded version of MP-ARC 96-263