The singularity spectrum for general Sierpiński carpets (Q1906987)

This paper is devoted to the study of the singularity spectrum of a class of two-dimensional Borel probability measures defined on general Sierpiński carpets, satisfying some disjointness condition (the singularity spectrum measures the variations of the local dimension of a measure). Even if Sierpiński carpets have a particular behaviour with respect to the one-dimensional case, the usual properties of the one-dimensional known examples of singularity spectrum are found here: the singularity spectrum is a smooth concave down function with a single critical point and is numerically computable as a Legendre transform.