The singularity spectrum of some non-regularity moran fractals

Abstract

In this paper, we shall study the multifractal decomposition behavior for a family of sets E known as Moran fractals. For each value of the parameter α ∈ ( α min, α max), we define “multifractal components” E α of E, and show that they are non-regularity fractals (in the sense of Taylor). By obtaining the new sufficient conditions for the valid multifractal formalisms of non-regularity Moran measures, we give explicit formula for the Hausdorff dimension and Packing dimension of E α respectively. In particular, we describe a large class of non-regularity Moran measure satisfying the explicit formula.