M. L. Lyra

NONEXTENSIVITY AND MULTIFRACTALITY IN LOW-DIMENSIONAL DISSIPATIVE SYSTEMS

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

Power-law sensitivity to initial conditions within a logisticlike family of maps: Fractality and nonextensivity

q

Lévy flight random searches in biological phenomena

. We show that general scaling arguments imply that

Correlation-induced metal-insulator transition in the one-dimensional Anderson model

1/(1-q) = 1/\alpha_{min}-1/\alpha_{max}

Bloch-Like Oscillations in a One-Dimensional Lattice with Long-Range Correlated Disorder

, where

Circular-like maps: sensitivity to the initial conditions, multifractality and nonextensivity

\alpha_{min}

Delocalization and spin-wave dynamics in ferromagnetic chains with long-range correlated random exchange

and

Delocalization in harmonic chains with long-range correlated random masses

\alpha_{max}

Wave-packet dynamics in chains with delayed electronic nonlinear response.

are the extremes of the multifractal singularity spectrum

The origin of fat tailed distributions in financial time series

f(\alpha)