Singularity spectra of strongly inhomogeneous multifractals

Abstract:

Generalized multifractal formalism is used to study singularity spectra of strongly inhomogeneous multifractals characterized by coarse-grained probability measures with zero minimal and/or infinite maximal Hölder exponents. Due to involving two additional types of scaling indices, the generalized formalism is shown to be able to describe complex multifractal objects by families of bivariate spectra rather than familiar single spectra of singularity strengths of one type, providing a more complete and adequate characteristics of such objects. It is proved that the families of extended singularity spectra can reveal unusual forms with many maxima, reflecting complex scaling structures of strongly inhomogeneous multifractals.