A Methodology for the Numerical Computation of Normal Forms, Centre Manifolds and First Integrals of Hamiltonian Systems

This paper deals with the e ective computation of normal forms, centre manifolds and rst integrals in Hamiltonian mechanics. These kind of calculations are very useful since they allow, for instance, to give explicit estimates on the di usion time or to compute invariant tori. The approach presented here is based on using algebraic manipulation for the formal series but taking numerical coe cients for them. This, jointly with a very e cient 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.