Fluctuation-Spectrum Approach to Anomalous Enhancement of Diffusive Motion in Chaotic Dynamics

Statistical dynamics of diffusive motions observed in the extended mapping system Xn+l = Xn +a·sin(2IlXn), and in the periodic potential system subject to the external excitation, X=-rX-sin(2IlX)+A·cos(Qt) is investigated for a situation just below the extinction points of diffusion. The sticking motion to certain regions of the map or the strange attractor causes the elongation of the duration of the hopping process. This produces the anomalous enhancement of diffusive motion. Its statistical analyses are carried out by observing the long·time statistical aspects of relevant temporal fluctuations from the fluctuation·spectrum viewpoint. We will find that scaling laws hold near the extinction point of diffusion for characteristic functions relevant to the present approach