3 papers
math.DS2025
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…
math.DS2024
Smoothness of random self-similar measures on the line and the existence of interior points
Balázs Bárány, Michał Rams
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…
math.DS2024
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 Śpiewak
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 eve…