Nonextensivity and multifractality in low-dimensional dissipative systems

Details Nonextensivity and multifractality in low-dimensional dissipative systems Nonextensivity and multifractality in low-dimensional dissipative systems

1997-09-20

arxiv.org/abs/cond-mat/9709226v1

Physics

Condensed Matter

Statistical Mechanics

12 pages, TeX, 4 ps figures

Scientific paper

10.1103/PhysRevLett.80.53

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 $1/(1-q) = 1/\alpha_{min}-1/\alpha_{max}$, where $\alpha_{min}$ and $\alpha_{max}$ are the extremes of the multifractal singularity spectrum $f(\alpha)$ 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.

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