98-6 Jorba A.

A Methodology for the Numerical Computation of Normal Forms, Centre Manifolds and First Integrals of Hamiltonian Systems (537K, PostScript (gzipped+uuencoded)) Jan 5, 98

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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).

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