Arnold diffusion for an a priori unstable Hamiltonian system with 3 + 1/2 degrees of freedom

Abstract

In this work we study the Arnold diffusion phenomenon on a concrete example of an a priori unstable Hamiltonian system with 3+1/2 degrees of freedom. Thanks to our mechanism, based on iterations of scattering and inner maps, rather than ensuring the existence of Arnold diffusion, we can present examples of diffusing orbits and estimate the diffusing time for some of these orbits. Throughout this paper, we use analytical methods supplemented by numerical calculations.