Fractional kinetics and accelerator modes

Kinetic properties of chaotic dynamics are studied for the web-map. It is shown that depending on the values of the perturbation parameter K, there are alternative possibilities: kinetics, of the quasilinear (normal, i.e. Gaussian) type or kinetics of the anomalous (Levyan) type. If K is close to the Values K = l pi when the accelerator modes occur, then there is superdiffusion with anomalous values of the transport exponent. We consider self-similar properties of trajectories near the islands in the phase space. Fractional kinetic equation is proposed and fractal exponents are obtained. Local properties of trajectories (exit time) and nonlocal ones (Poincare cycles) are studied and compared for the normal and anomalous kinetics. It is shown that the power-like law of the trapping distribution function imposes the same kind of asymptotics for the Poincare cycles distribution.