FM: 1994-08 (mp_arc 94-92)

Author : Guido Gentile

Title: Whiskered tori with prefixed frequencies and Lyapunov spectrum

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.

Keywords: Whiskered tori, Lyapunov spectrum

Guido Gentile
Dipartimento di Matematica, Università di Roma Tre
L. S. Leonardo Murialdo
00100 Roma, Italia
tel +39-06-54-888-226