Three or More Degrees of Freedom

Abstract

We have seen that resonances between oscillators in two degrees of freedom lead to the formation of a dense set of resonance layers in the action space. Within each layer, stochastic motion exists. However, energy conservation prevents large excursions of the motion along the layer. Only motion across the layer is important. For a near-integrable system with a weak perturbation, the stochastic layers are isolated by KAM surfaces.