On the onset of chaotic motion in deterministic systems

摘要

In the present paper the classical counterpart of the quantum avoided crossing method for detecting chaos is described using classical (Liehyphen;transform) perturbation theory and a grid of action variables. The results are applied to two systems of coupled oscillators with cubic and quartic nonlinearities. The plots of energy of members of the grid versus the perturbation parameter provide a visual description for predicting the onset of chaos.