Gibbs attractor: a chaotic nearly Hamiltonian system, driven by external harmonic force
Abstract
A chaotic autonomous Hamiltonian systems, 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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.