Application of Tsallis Nonextensive Statistics to the Anomalous Diffusion of the Standard Map

The anomalous diffusion due to accelerator-mode islands in the Standard Map is analyzed with the aid of Tsallis nonextensive statistics. In this treatment, we introduce a new variable x, which represents the displacement per jump while the chaotic orbit is trapped by the accelerator-mode islands. We have shown numerically that the one-jump distribution function p(x) is qualitatively similar to the function pq(x) derived using the maximum Tsallis entropy principle with appropriate conditions. [C. Tsallis, J. Stat. Phys. 52 (1988), 479; Phys. Lett. A 195 (1994), 329.] We find that the n-jump distribution function p(x, n) converges to the n-jump distribution function pq(x, n )= 1 n1/γ pq( x n1/γ ) obtained from the