On the constructivity of the variational approach to Arnold’s Diffusion

Abstract

The aim of this paper is to discuss the constructivity of the method originally introduced by U. Bessi to approach the phenomenon of topological instability commonly known as Arnold’s Diffusion. By adapting results and proofs from existing works and introducing additional tools where necessary, it is shown how, at least for a (well known) paradigmatic model, it is possible to obtain a rigorous proof on a suitable discrete space, which can be fully implemented on a computer. A selection of explicitly constructed diffusing trajectories for the system at hand is presented in the final section.