Topological instability along filamented invariant surfaces

In dynamical systems with a zero Lyapunov exponent, weak mixing can be governed by a specific topological structure of some surfaces that are invariant with respect to particle dynamics. In particular, when the genus of the invariant surfaces is more than one, they may have weak mixing and the corresponding fractional kinetics. This possibility is demonstrated by using a typical example from plasma physics, a three-dimensional resistive pressure-gradient-driven turbulence model. In a toroidal geometry and with a low-pressure gradient, this model shows the emergence of quasicoherent structures. In this situation, the isosurfaces of the velocity stream function have a web structure with filamentary surfaces emerging from the outer region of the torus and covering the inner region. The filamentary surfaces can result in stochastic jets of particles that cause a "topological instability." In such a situation, particle transport along the surfaces is of the anomalous superdiffusion type.