Discrete wavelet approach to multifractality

A new and simple method is presented to study local scaling properties of measures defined on regular and fractal supports. The method, based on a discrete wavelet analysis (WA), complements the well-known multifractal analysis (MA) extensively used in many physical problems. The present wavelet approach is particularly suitable for problems where the multifractal analysis does not provide conclusive results, as e.g. in the case of measures corresponding to Anderson localized wave-functions in one-dimension. Examples of different types of measures are also discussed which illustrate the usefulness of the WA to classify non-multifractal measures according to additional characteristic exponents, which can not be obtained within the MA.