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math.DS2024
Fibre stability for dominated self-affine sets
Roope Anttila, Alex Rutar
Let be a planar self-affine set. Assuming a weak domination condition on the matrix parts, we prove for all backward Furstenberg directions that $$\max_{E\in\operatorname{T…
math.DS2024
Multifractal analysis for the pointwise Assouad dimension of self-similar measures
Roope Anttila, Ville Suomala
We quantify the pointwise doubling properties of self-similar measures using the notion of pointwise Assouad dimension. We show that all self-similar measures satisfying the open s…