6 citations · 6 across the 2 of their papers we have counts for
9 papers
On the Marstrand projection theorem for the Assouad spectrum
Kenneth J. Falconer, Jonathan M. Fraser, Antti Käenmäki
Marstrand's projection theorem states that the Hausdorff dimension of the orthogonal projection of a Borel set in the plane onto lines is constant almost surely. This property exte…
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…
Finer geometry of planar self-affine sets
Balázs Bárány, Antti Käenmäki, Han Yu
For planar self-affine sets satisfying the strong separation condition, recent work of Bárány, Hochman, and Rapaport gives mild assumptions under which the Hausdorff dimension eq…
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…
Level sets of prevalent Weierstrass functions
Zoltán Buczolich, Antti Käenmäki, Balázs Maga
The -Weierstrass function is defined as , where is a Lipschitz function on the unit circle. For a prevalent -Weie…
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…