Guido Gentile
Whiskered tori with prefixed frequencies and Lyapunov spectrum
(143K, Plain Tex)
ABSTRACT. A classical mechanics problem, as the existence
of whiskered tori for an almost integrable hamiltonian system, is analyzed
with techniques reminiscent of the quantum field theory, following the
strategy developed in recent works about the matter. The system consists
in a collection of rotators interacting with a pendulum via a small
potential depending only on the angle variables. The proof of the
existence of the stable and unstable manifolds (``whiskers") of the
rotators invariant tori corresponding to diophantine rotation numbers
is simplified by setting the Lyapunov spectrum to prefixed values via
the introduction, in the hamiltonian function, of ``counterterms"
depending on the strength of the interaction;
this is a feature usual in quantum field theory,
and emphasizes the analogy between the the field theory and the KAM
framework pointed out already in the mentioned works.