1997/09/20 by M. L. Lyra, C. Tsallis · 1 citation
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.80.53
12 pages, TeX, 4 ps figures
arxiv created 1997/09/20 · arxiv updated 2016/08/31
Power-law sensitivity to initial conditions at the edge of chaos provides a natural relation between the scaling properties of the dynamics attractor and its degree of nonextensivity as prescribed in the generalized statistics recently introduced by one of us (C.T.) and characterized by the entropic index q. We show that general scaling arguments imply that 1/(1-q) = 1/αmin-1/αmax, where αmin and αmax are the extremes of the multifractal singularity spectrum f(α) of the attractor. This relation is numerically checked to hold in standard one-dimensional dissipative maps. The above result sheds light on a long-standing puzzle concerning the relation between the entropic index q and the underlying microscopic dynamics.