8 papers
Hausdorff measure of dominated planar self-affine sets with large dimension
Balázs Bárány
In this paper, we investigate the Hausdorff measure of planar dominated self-affine sets at their affinity dimension. We show that the Hausdorff measure being positive and finite i…
Self-affine sponges with random contractions
Balázs Bárány, Antti Käenmäki, MichaŠRams
We compute the almost sure Hausdorff dimension of random self-affine sponges in without imposing any separation conditions. In this context, randomness arises from t…
On the dimension theory of Okamoto's function
Balázs Bárány, R. Dániel Prokaj
In this paper, we investigate the dimension theory of the one parameter family of Okamoto's function. We compute the Hausdorff, box-counting and Assouad dimensions of the graph for…
Universal projection theorems with applications to multifractal analysis and the dimension of every ergodic measure on self-conformal sets simultaneously
Balázs Bárány, Károly Simon, Adam Åpiewak
We prove a universal projection theorem, giving conditions on a parametrized family of maps and a collection M of measures on X under which for almost e…
Smoothness of random self-similar measures on the line and the existence of interior points
Balázs Bárány, MichaŠRams
In this paper, we study the smoothness of the density function of absolutely continuous measures supported on random self-similar sets on the line. We show that the natural project…
On an abrasion motivated fractal model
Balázs Bárány, Gábor Domokos, Ãgoston Szesztay
In this paper, we consider a fractal model motivated by the abrasion of convex polyhedra, where the abrasion is realised by chipping small neighbourhoods of vertices. After providi…