Intermittency, ergodicity, and spectral analysis in classical Hamiltonian dynamics

A generic mechanism for intermittency in two-dimensional bounded Hamiltonian dynamics (with two different time scales) is analyzed. This analysis sheds some light on the importance of tori jumps as a source of chaos. We show how intermittency arises in the systems considered, and by using ergodic considerations we estimate the distribution of laminar lengths. The phenomenology found shares features corresponding to both type-I and type-II intermittency. The intermittent behavior is then used to model the dynamics as an incoherent superposition of laminar periods. We derive a formula for the frequency spectrum based on this model and on ergodic theory. All the results predicted are tested on a concrete system.