1 citations · 1 across the 13 of their papers we have counts for
9 papers · 1 filter
Multifractal analysis of Gatzouras--Lalley measures
Thomas Jordan, István Kolossváry, Alex Rutar
We study the multifractal analysis of self-affine measures supported on planar carpets of type Gatzouras--Lalley. We work primarily with Olsen's Hausdorff-dimensional variant of th…
Two-scale branching functions and inhomogeneous attractors
Vilma Orgoványi, Alex Rutar
We introduce the notion of a two-scale branching function associated with an arbitrary metric space, which encodes the lower and upper box dimensions as well as the Assouad spectru…
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…
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…
Multifractal analysis via Lagrange duality
Alex Rutar
We provide a self-contained exposition of the well-known multifractal formalism for self-similar measures satisfying the strong separation condition. At the heart of our method lie…
Tangents of invariant sets
Antti Käenmäki, Alex Rutar
We study the fine scaling properties of sets satisfying various weak forms of invariance. For general attractors of possibly overlapping bi-Lipschitz iterated function systems, we…