Alex Rutar

activity

20232026

most citedTangents and slices of self-affine carpets

1 citations · 1 across the 13 of their papers we have counts for

collaborators

14 papers

math.DS2026

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…

math.NT2026

Multi-scale properties of continued fraction sets

Alex Rutar

We survey the dimension theory of sets of real numbers with regular continued fraction expansion restricted to a non-empty and possibly infinite subset $\mathcal{D}\subset\mathbb{N…

math.CO2026

Visibility problem in the plane

Tuomas Orponen, Alex Rutar

We disprove the visibility conjecture in the plane and prove the sharp upper bound for the almost-sure dimension of visible parts. Precisely, let $K \subset R^{2}$ be a co…

math.CA2026

Attainable forms of lower spectra

Amlan Banaji, Haipeng Chen, Alex Rutar +1

Let $d \in N$ and $φ : (0, 1) \to [0, d]$ . We prove there exists a set $F \subset R^{d}$ whose lower spectrum $dim_{L}^{θ} F$ satisfies $(1-θ)\oper…

math.DS2025

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…

math.CA2025

A fractal local smoothing problem for the wave equation

David Beltran, Joris Roos, Alex Rutar +1

For any given set $E \subset [1, 2]$ , we discuss a fractal frequency-localized version of the $L^{p}$ local smoothing estimates for the half-wave propagator with times in $E$ . A conjec…

math.DS2024

Fibre stability for dominated self-affine sets

Roope Anttila, Alex Rutar

Let $K$ be a planar self-affine set. Assuming a weak domination condition on the matrix parts, we prove for all backward Furstenberg directions $V$ that $$\max_{E\in\operatorname{T…

math.MG2024

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 $K \subset R^{d}$ with Assouad dimen…

math.DS2024★ 1 cited

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…

math.DS2024

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…

math.DS2024

Lower box dimension of infinitely generated self-conformal sets

Amlan Banaji, Alex Rutar

Let $Λ$ be the limit set of an infinite conformal iterated function system and let $F$ denote the set of fixed points of the maps. We prove that the box dimension of $Λ$ exists if…

math.DS2024

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…

math.DS2023

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…

math.DS2023

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…