NONEXTENSIVITY AND MULTIFRACTALITY IN LOW-DIMENSIONAL DISSIPATIVE SYSTEMS

Power-law sensitivity to the initial conditions at the edge of chaos p rovides a natural relation between the scaling properties of the dynam ics attractor and its degree of nonextensivity within the generalized statistics recently introduced by one of the authors (C.T.) and charac terized by the entropic index q. We show that general scaling argument s imply that 1/(1 -q) = 1/alpha(min) -1/alpha(max), where alpha(min) a nd alpha(max) are the extremes of the multifractal singularity spectru m f(alpha) of the attractor. This relation is numerically verified in standard D = 1 dissipative maps.