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 …

We extend the study of the multifractal analysis of the class of equicontractive self-similar
measures of finite type to the non-equicontractive setting. Although stronger than the weak …

Consider a finite sequence of linear contractions and probabilities tends to infinity. Lastly, we
show that within a maximal loop class that is not truly essential, the set of upper local …

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 …

We study sets of local dimensions for self-similar measures in $\mathbb {R} $ satisfying the
finite neighbour condition, which is formally stronger than the weak separation condition …

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 …

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 …