Construction of Whiskers for the Quasiperiodically Forced Pendulum

TL;DR

This paper develops a method to construct unstable KAM tori and their manifolds in a Hamiltonian system combining a pendulum with oscillators, extending solutions analytically near the time axis for small perturbations.

Contribution

It provides a novel construction of unstable KAM tori and their manifolds in a coupled pendulum-oscillator Hamiltonian system, with an analytical extension of solutions.

Findings

Construction of unstable KAM tori and manifolds

Analytical extension of solutions near the time axis

Applicability to analytic perturbations

Abstract

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. We extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a uniform neighbourhood of the time axis.