Transport near the onset of stochasticity

For two-degree-of-freedom Hamiltonians, (e.g., a particle in a 2-D potential or the flow of magnetic field lines) an invariant torus in phase space acts as an absolute barrier for trajectories. When an invariant torus is destroyed by a perturbation, a remnant remains with gaps. This ''cantorus'' forms a formidable barrier even well into the stochastic regime. We show that correlation functions decay algebraically invalidating the common assumptions of chaos. The decay rate is given by a universal exponent, obtained from self-similar scaling