4 papers
Badly approximable points on non-linear carpets
Roope Anttila, Jonathan M. Fraser, Henna Koivusalo
The badly approximable points in are those for which Dirichlet's approximation theorem cannot be improved by more than a constant, that is, they are the points most…
Dvoretzky covering problem for general measures
Roope Anttila, Markus Myllyoja
We study the Dvoretzky covering problem for random covering sets driven by general Borel probability measures. As our main result, we solve the problem of covering analytic sets by…
Quasisymmetric mappings on two variants of fractal percolation
Roope Anttila, Sylvester Eriksson-Bique, Aleksi Pyörälä
We study quasisymmetric maps on two variants of the classical fractal percolation model: the fat and dense fractal percolations. We show that, almost surely conditioned on non-exti…
Fibre stability for dominated self-affine sets
Roope Anttila, Alex Rutar
Let be a planar self-affine set. Assuming a weak domination condition on the matrix parts, we prove for all backward Furstenberg directions that $$\max_{E\in\operatorname{T…