Unusual manifold structure and anomalous diffusion in a Hamiltonian model for chaotic guiding-center motion

We report some unusual dynamical phenomena found in a Hamiltonian system of 1.5 degrees of freedom. The Hamiltonian describes the guiding-center motion of a charged particle in the presence of three electrostatic waves. There is a collapse of two hyperbolic fixed points into one, which gives rise to a mechanism for the onset of large-scale stochasticity. A nonlinear stability analysis demonstrates the existence of three invariant manifolds at the collapsed point. With increasing perturbation the large-scale chaotic motion exhibits anomalous diffusion with a ${\mathit{t}}^{1/3}$ growth of the variance, which is explained by trapping in a hierarchy of nested cantori.