63 citations · 156 across the 13 of their papers we have counts for
6 papers · 1 filter
On the Hausdorff measure of shrinking target sets on self-conformal sets
Demi Allen, Balázs Bárány
In this article, we study the Hausdorff measure of shrinking target sets on self-conformal sets. The Hausdorff dimension of the sets we are interested in here was established by Hi…
Super-exponential condensation without exact overlaps
Balázs Bárány, Antti Käenmäki
We exhibit self-similar sets on the line which are not exponentially separated and do not generate any exact overlaps. Our result shows that the exponential separation, introduced…
Assouad dimension of planar self-affine sets
Balázs Bárány, Antti Käenmäki, Eino Rossi
We calculate the Assouad dimension of a planar self-affine set satisfying the strong separation condition and the projection condition and show that is minimal for the conf…
On the dimension of self-similar measures with complicated overlaps
Balázs Bárány, Edina Szvák
In this paper, we investigate the Hausdorff dimension of the invariant measures of the iterated function system (IFS) . We provide an "almost every" type resu…
Dimension Theory of some non-Markovian repellers Part II: Dynamically defined function graphs
Balázs Bárány, Michał Rams, Károly Simon
This is the second part in a series of two papers. Here, we give an overview on the dimension theory of some dynamically defined function graphs, like Takagi and Weierstrass functi…
Dimension Theory of some non-Markovian repellers Part I: A gentle introduction
Balázs Bárány, Michał Rams, Károly Simon
Michael Barnsley introduced a family of fractals sets which are repellers of piecewise affine systems. The study of these fractals was motivated by certain problems that arose in f…