68 citations · 131 across the 11 of their papers we have counts for
18 papers
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…
Absolute continuity in families of parametrised non-homogeneous self-similar measures
Antti Käenmäki, Tuomas Orponen
Let be a planar self-similar measure with similarity dimension exceeding , satisfying a mild separation condition, and such that the fixed points of the associated similitud…
Attainable values for the Assouad dimension of projections
Jonathan M. Fraser, Antti Käenmäki
We prove that for an arbitrary upper semi-continuous function there exists a compact set in the plane such that for all…
On the Hausdorff dimension of microsets
Jonathan M. Fraser, Douglas C. Howroyd, Antti Käenmäki +1
We investigate how the Hausdorff dimensions of microsets are related to the dimensions of the original set. It is known that the maximal dimension of a microset is the Assouad dime…
Birkhoff and Lyapunov spectra on planar self-affine sets
Balázs Bárány, Thomas Jordan, Antti Käenmäki +1
Working on strongly irreducible planar self-affine sets satisfying the strong open set condition, we calculate the Birkhoff spectrum of continuous potentials and the Lyapunov spect…