17 citations · 47 across the 9 of their papers we have counts for
9 papers
Interpolating with generalized Assouad dimensions
Amlan Banaji, Alex Rutar, Sascha Troscheit
The -Assouad dimensions are a family of dimensions which interpolate between the upper box and Assouad dimensions. They are a generalization of the well-studied Assouad spectrum…
Multifractal analysis of measures arising from random substitutions
Andrew Mitchell, Alex Rutar
We study regularity properties of frequency measures arising from random substitutions, which are a generalisation of (deterministic) substitutions where the substituted image of e…
Assouad-type Dimensions of Overlapping Self-affine Sets
Jonathan M. Fraser, Alex Rutar
We study the Assouad and quasi-Assoaud dimensions of dominated rectangular self-affine sets in the plane. In contrast to previous work on the dimension theory of self-affine sets,…
Attainable forms of Assouad spectra
Alex Rutar
Let and let . We prove that there exists a set such that for all if and onl…
Attainable forms of intermediate dimensions
Amlan Banaji, Alex Rutar
The intermediate dimensions are a family of dimensions which interpolate between the Hausdorff and box dimensions of sets. We prove a necessary and sufficient condition for a given…
A Multifractal Decomposition for Self-similar Measures with Exact Overlaps
Alex Rutar
We study self-similar measures in satisfying the weak separation condition along with weak technical assumptions which are satisfied in all known examples. For such a…
Local Dimensions of Self-similar Measures Satisfying the Finite Neighbour Condition
Kathryn E. Hare, Alex Rutar
We study sets of local dimensions for self-similar measures in satisfying the finite neighbour condition, which is formally stronger than the weak separation condition…
Geometric and Combinatorial Properties of Self-similar Multifractal Measures
Alex Rutar
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 de…
When the Weak Separation Condition implies the Generalized Finite Type Condition
Kathryn E. Hare, Kevin G. Hare, Alex Rutar
We prove that an iterated function system of similarities on that satisfies the weak separation condition and has an interval as its self-similar set satisfies the str…