68 citations · 131 across the 12 of their papers we have counts for
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Self-affine sponges with random contractions
Balázs Bárány, Antti Käenmäki, Michał Rams
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…
Thermodynamic formalism of countably generated self-affine sets
Antti Käenmäki, Ian D. Morris
In this article, we further develop the thermodynamic formalism of affine iterated function systems with countably many transformations by showing the existence and extending earli…
Local dimension spectrum for dominated planar self-affine sets
Alex Batsis, Antti Käenmäki, Tom Kempton
The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this…
Tangents of invariant sets
Antti Käenmäki, Alex Rutar
We study the fine scaling properties of sets satisfying various weak forms of invariance. For general attractors of possibly overlapping bi-Lipschitz iterated function systems, we…
Scaling limits of self-conformal measures
Balázs Bárány, Antti Käenmäki, Aleksi Pyörälä +1
We show that any self-conformal measure on is uniformly scaling and generates an ergodic fractal distribution. This generalizes existing results by removing the ne…
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…