Jorba A.
A Methodology for the Numerical Computation of Normal Forms,
Centre Manifolds and First Integrals of Hamiltonian Systems
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ABSTRACT.  This paper deals with the effective computation of normal forms,
centre manifolds and first integrals in Hamiltonian mechanics. These
kind of calculations are very useful since they allow, for instance,
to give explicit estimates on the diffusion time or to compute
invariant tori. The approach presented here is based on using
algebraic manipulation for the formal series but taking numerical
coefficients for them. This, jointly with a very efficient
implementation of the software, allows big savings in both memory and
execution time of the algorithms if we compare with the use of
commercial algebraic manipulators. The algorithms are presented
jointly with their C/C++ implementations, and they are applied to some
concrete examples coming from celestial mechanics.
The corresponding software has been put in the public domain, and it
can be obtained from the web server http://www.maia.ub.es/dsg in the
preprints section (year 1998).