Gibbs attractor: A chaotic nearly Hamiltonian system, driven by external harmonic force

A chaotic autonomous Hamiltonian system, perturbed by small damping and small external force, harmonically dependent on time, can acquire a strange attractor with properties similar to that of the canonical distribution--the Gibbs attractor. The evolution of the energy in such systems can be described as the energy diffusion. For the nonlinear Pullen-Edmonds oscillator with two degrees of freedom, the properties of the Gibbs attractor and their dependence on parameters of the perturbation are studied both analytically and numerically.