Arnold diffusion for a complete family of perturbations with two independent harmonics

TL;DR

This paper proves that any non-trivial perturbation involving two independent harmonics causes global instability in a pendulum and rotor system, using geometric methods and scattering maps.

Contribution

It introduces a comprehensive geometric approach and detailed scattering map analysis to establish global instability for a broad class of perturbations.

Findings

Global instability for all non-trivial two-harmonic perturbations

Explicit computation and description of scattering maps

Existence of piecewise smooth global scattering maps

Abstract

We prove that for any non-trivial perturbation depending on any two independent harmonics of a pendulum and a rotor there is global instability. The proof is based on the geometrical method and relies on the concrete computation of several scattering maps. A complete description of the different kinds of scattering maps taking place as well as the existence of piecewise smooth global scattering maps is also provided.