Whiskered tori with prefixed frequencies and Lyapunov spectrum

Abstract

A classical mechanics problemthe existence of whiskered tori for an almost integrable Hamiltonian systemis analyzed with techniques reminiscent of the quantum field theoryfollowing the strategy developed in recent worksThe system consists of a collection of rotators interacting with a pendulum via a small potential depending only on the angle variablesThe proof of the existence of the stable and unstable manifolds (‘whiskers’) of the rotators invariant tori corresponding to dio- phantine rotation numbers is simplified by setting the Lyapunov spectrum to prefixed values via the introductionin the Hamiltonian functionof‘counterterms7 depending on the strength of the interaction; this is a feature usual in quantum field theoryand emphasizes the analogy between the field theory and the KAM framework pointed out already in the mentioned works