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math.MG2021★ 17 cited
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…
math.DS2021★ 1 cited
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…
math.DS2021★ 3 cited
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…