A. Käenmäki

works on

fractal dimensions 1 Hausdorff dimension 1 Minkowski dimension 1 projection theorems 1 self-affine sets 1

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math.DS2026

Covering number on inhomogeneous graph-directed self-similar sets

BalÃ¡zs BÃ¡rÃ¡ny, Antti KÃ¤enmÃ¤ki, Petteri Nissinen

For a strongly connected inhomogeneous graph-directed self-similar set $K^{C}$ satisfying the strong open set condition, we characterize the asymptotic behaviour of the $r$ -covering…

math.DS2025

Regularity of non-autonomous self-similar sets

Antti KÃ¤enmÃ¤ki, 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…

math.DS2024

Dimension of planar non-conformal attractors with triangular derivative matrices

BalÃ¡zs BÃ¡rÃ¡ny, Antti KÃ¤enmÃ¤ki

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…