article-journal

Intermediate dimensions of Bedford–McMullen carpets with applications to Lipschitz equivalence
Intermediate dimensions were introduced to provide a spectrum of dimensions interpolating between Hausdorff and box-counting dimensions …
Amlan Banaji, István Kolossváry
Cite DOI arXiv zbMATH
The Assouad dimension of self-affine measures on sponges
We derive upper and lower bounds for the Assouad and lower dimensions of self-affine measures in $\mathbb{R}^d$ generated by diagonal …
Jonathan M. Fraser, István Kolossváry
Cite DOI arXiv zbMATH
The $L^q$ spectrum of self-affine measures on sponges
In this paper, a sponge in $\mathbb{R}^d$ is the attractor of an iterated function system consisting of finitely many strictly …
István Kolossváry
Cite DOI arXiv zbMATH
On the Convergence Rate of the Chaos Game
This paper studies how long it takes the orbit of the chaos game to reach a certain density inside the attractor of a strictly …
Balázs Bárány, Natalia Jurga, István Kolossváry
Cite DOI arXiv zbMATH
An upper bound for the intermediate dimensions of Bedford-McMullen carpets
The intermediate dimensions of a set $\Lambda$, elsewhere denoted by $\dim_{\theta} \Lambda$, interpolate between its Hausdorff and box …
István Kolossváry
Cite DOI arXiv zbMATH
Distance between natural numbers based on their prime signature
We define a new metric between natural numbers induced by the $\ell_\infty$ norm of their unique prime signatures. In this space, we …
István B. Kolossváry, István Kolossváry
Cite DOI arXiv zbMATH
Hausdorff measure and Assouad dimension of generic self-conformal IFS on the line
This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space …
Balázs Bárány, István Kolossváry, Mihał Rams, Károly Simon
Cite DOI arXiv zbMATH
Triangular Gatzouras–Lalley-type planar carpets with overlaps
We construct a family of planar self-affine carpets with overlaps using lower triangular matrices in a way that generalizes the …
István Kolossváry, Károly Simon
Cite DOI arXiv zbMATH
Pointwise regularity of parameterized affine zipper fractal curves
We study the pointwise regularity of zipper fractal curves generated by affine mappings. Under the assumption of dominated splitting of …
Balázs Bárány, Gergely Kiss, István Kolossváry
Cite Poster DOI arXiv zbMATH
Degrees and distances in random and evolving Apollonian networks
In this paper we study random Apollonian networks (RANs) and evolving Apollonian networks (EANs), in $d$ dimensions for any $d\geq 2$, …
István Kolossváry, Júlia Komjáthy, Lajos Vágó
Cite DOI arXiv zbMATH