Inverse problem for multifractals: extension to logarithmic and additive corrections

Abstract

We extend the inverse problem for multifractals to include the generalized logarithmic dimensions and the generalized metadimensions. These dimensions are shown to contribute characteristic n-dependent corrections to the scaling function, where n is the stage of scaling refinement. We establish a connection between these corrections and the type of dimensions and demonstrate the utility of such a connection in the specific case of one-dimensional maps.