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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…
On the uniformity and size of microsets
Richárd Balka, Vilma Orgoványi, Alex Rutar
We resolve a few questions regarding the uniformity and size of microsets of subsets of Euclidean space. First, we construct a compact set with Assouad dimen…
Tangents and slices of self-affine carpets
Antti Käenmäki, Alex Rutar
We study the fine scaling properties of planar self-affine carpets. For Gatzouras--Lalley carpets, we give a precise formula for maximal Hausdorff dimension of a tangent in terms o…
Regularity of non-autonomous self-similar sets
Antti Käenmäki, Alex Rutar
Non-autonomous self-similar sets are a family of compact sets which are, in some sense, highly homogeneous in space but highly inhomogeneous in scale. The main purpose of this note…
Lower box dimension of infinitely generated self-conformal sets
Amlan Banaji, Alex Rutar
Let be the limit set of an infinite conformal iterated function system and let denote the set of fixed points of the maps. We prove that the box dimension of exists if…
Assouad spectrum of Gatzouras-Lalley carpets
Amlan Banaji, Jonathan M. Fraser, István Kolossváry +1
We study the fine local scaling properties of a class of self-affine fractal sets called Gatzouras-Lalley carpets. More precisely, we establish a formula for the Assouad spectrum o…