Nonextensivity and Multifractality in Low-Dimensional Dissipative Systems

Power-law sensitivity to the initial conditions at the edge of chaos provides a natural relation between the scaling properties of the dynamics attractor and its degree of nonextensivity within the generalized statistics recently introduced by one of the authors (C.T.) and characterized by the entropic index q. We show that general scaling arguments imply that 1/(1-q)0ex0ex=0ex0ex1/αₘᵢₙ-1/αₘₐₓ, where αₘᵢₙ and αₘₐₓ are the extremes of the multifractal singularity spectrum f(α) of the attractor. This relation is numerically verified in standard D0ex0ex=0ex0ex1 dissipative maps.