Complex multifractal measures and a generalized multifractal formalism

Strongly inhomogeneous multifractal measures involving extremely diverse lo cal probability scales and exhibiting left-sided multifractal spectra are c onsidered. The standard multifractal formalism is extended to such drastica lly inhomogeneous multifractal measures by introducing additional filtering variables and scaling exponents, conjugated to these variables. It is show n that the generalized multifractal formalism provides a more adequate and complete description of complex structures of strongly inhomogeneous multif ractal measures, in comparison with conventional formalism. (C) 2001 Elsevi er Science B.V. All rights reserved.