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 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 …

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 …

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 …

Uniformity of Lyapunov exponents for non-invertible matrices Page 1 Ergod. Th. & Dynam. Sys.
(2020), 40, 2399–2433 doi:10.1017/etds.2019.4 c Cambridge University Press, 2019 Uniformity …

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 …