Geometric identities with applications to computational KAM theory.
Rafael de la Llave
KAM theory seeks quasi-periodic solutions in
When the systems preserve a geometric structure
(symplectic, volume, conformal symplectic) or
admit a variational formulation, there are
We use these identities a) to obtain very
efficient algorithms (they are quasi-newton
steps, with small storage or operation counts)
b) to obtain "a posteriori" theorems
which say that near computed solutions (which
have reasonable condition numbers) there are
The algorithms have been implemented and they lead to
some conjectures about breakdown.
Joint work with: R. Calleja, E. Fontich, A. Gonzalez-Enriquez,
G. Huguet, Y. Sire