Self-similar sets require a separation condition to admit a nice mathematical structure. The
classical open set condition (OSC) is difficult to verify. Zerner proved that there is a positive …

In analogy with the lower Assouad dimensions of a set, we study the lower Assouad
dimensions of a measure. As with the upper Assouad dimensions, the lower Assouad …

We prove that an iterated function system of similarities on $\mathbb {R} $ that satisfies the
weak separation condition and has an interval as its self-similar set is of generalized finite …

We establish matrix representations for self-similar measures on R d generated by
equicontractive IFSs satisfying the finite type condition. As an application, we prove that the …

Abstract The Assouad and quasi-Assouad dimensions of a metric space provide information
about the extreme local geometric nature of the set. The Assouad dimension of a set has a …

We study self-similar measures in $\mathbb {R} $ satisfying the weak separation condition
along with weak technical assumptions which are satisfied in all known examples. For such …

The upper and lower Assouad dimensions of a metric space are local variants of the box
dimensions of the space and provide quantitative information about the 'thickest'and …

It is known that the heuristic principle, referred to as the multifractal formalism, need not hold
for self-similar measures with overlap, such as the $3 $-fold convolution of the Cantor …

In this paper, we investigate p-adic self-similar sets and p-adic self-similar measures. We
introduce a condition (C) under which p-adic self-similar sets can be shown to have a …

For any self-similar measure in, we show that the distribution of is controlled by products of
non-negative matrices governed by a finite or countable graph depending only on the …