44 citations · 88 across the 3 of their papers we have counts for
6 papers · 1 filter
Tangents and slices of self-affine carpets
Antti Käenmäki, Alex Rutar
We study the fine scaling properties of planar self-affine carpets. For Gatzouras--Lalley carpets, we give a precise formula for maximal Hausdorff dimension of a tangent in terms o…
Regularity of non-autonomous self-similar sets
Antti Käenmäki, Alex Rutar
Non-autonomous self-similar sets are a family of compact sets which are, in some sense, highly homogeneous in space but highly inhomogeneous in scale. The main purpose of this note…
Dimension of planar non-conformal attractors with triangular derivative matrices
Balázs Bárány, Antti Käenmäki
We study the dimension of the attractor and quasi-Bernoulli measures of parametrized families of iterated function systems of non-conformal and non-affine maps. We introduce a tran…
Covering number on inhomogeneous graph-directed self-similar sets
Balázs Bárány, Antti Käenmäki, Petteri Nissinen
For a strongly connected inhomogeneous graph-directed self-similar set satisfying the strong open set condition, we characterize the asymptotic behaviour of the -covering…
Domination, almost additivity, and thermodynamic formalism for planar matrix cocycles
Balázs Bárány, Antti Käenmäki, Ian D. Morris
In topics such as the thermodynamic formalism of linear cocycles, the dimension theory of self-affine sets, and the theory of random matrix products, it has often been found useful…
Dimension and measures on sub-self-affine sets
Antti Käenmäki, Markku Vilppolainen
We show that in a typical sub-self-affine set, the Hausdorff and the Minkowski dimensions coincide and equal the zero of an appropriate topological pressure. This gives a partial p…