The Melnikov Technique and Arnold Diffusion for a Class of Perturbed Dissipative Systems

This work presents a slight extension to the vector Melnikov function that measures the presence of Arnold diffusion in perturbed near-integrable Hamiltonian systems. It adopts a differential equations viewpoint and allows one subsystem, the one possessing the homoclinic orbit, to be dissipative. Adding damping to the other subsystems appears very difficult because of the Hamiltonian nature of KAM theory. This extension is made with a view to application.