Dimension

Assouad spectrum of Gatzouras-Lalley carpets
We study the fine local scaling properties of a class of self-affine fractal sets called Gatzouras-Lalley carpets. More precisely, we …
Amlan Banaji, Jonathan M. Fraser, István Kolossváry, Alex Rutar
Cite Project DOI arXiv zbMATH
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
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
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